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Circumference and Wheels
Let’s explore how far different wheels roll.
The diameter of a bike wheel is 27 inches. If the wheel makes 15 complete rotations, how far does the bike travel?
The wheels on Kiran's bike are 64 inches in circumference. How many times do the wheels rotate if Kiran rides 300 yards?
The numbers are measurements of radius, diameter, and circumference of circles A and B. Circle A is smaller than circle B. Which number belongs to which quantity?
2.5, 5, 7.6, 15.2, 15.7, 47.7
Circle A has circumference \(2\frac23\) m. Circle B has a diameter that is \(1\frac12\) times as long as Circle A’s diameter. What is the circumference of Circle B?
The length of segment \(AE\) is 5 centimeters.
- What is the length of segment \(CD\)?
- What is the length of segment \(AB\)?
- Name a segment that has the same length as segment \(AB\).
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Virasoro algebra explained
In mathematics, the Virasoro algebra (named after the physicist Miguel Ángel Virasoro) is a complex Lie algebra and the unique central extension of the Witt algebra. It is widely used in two-dimensional conformal field theory and in string theory.
The Virasoro algebra is spanned by generators for and the central charge .These generators satisfy
and The factor of
is merely a matter of convention. For a derivation of the algebra as the unique central extension of the Witt algebra
, see derivation of the Virasoro algebra.
The Virasoro algebra has a presentation in terms of two generators (e.g. 3 and −2) and six relations.
Highest weight representations
A highest weight representation of the Virasoro algebra is a representation generated by a primary state: a vector
where the number is called the conformal dimension or conformal weight of
A highest weight representation is spanned by eigenstates of
. The eigenvalues take the form
, where the integer
is called the level of the corresponding eigenstate.
More precisely, a highest weight representation is spanned by
-eigenstates of the type
, whose levels are
. Any state whose level is not zero is called a descendant state of
is the largest possible highest weight representation. (The same letter is used for both the element of the Virasoro algebra and its eigenvalue in a representation.)
form a basis of the Verma module. The Verma module is indecomposable, and for generic values of and it is also irreducible. When it is reducible, there exist other highest weight representations with these values of and, called degenerate representations, which are cosets of the Verma module. In particular, the unique irreducible highest weight representation with these values of and is the quotient of the Verma module by its maximal submodule.
A Verma module is irreducible if and only if it has no singular vectors.
A singular vector or null vector of a highest weight representation is a state that is both descendent and primary.
A sufficient condition for the Verma module
to have a singular vector at the level
for some positive integers
)2-(br+b-1s)2) , where c=1+6(b+b-1)2 .
, and the reducible Verma module
has a singular vector
at the level
, and the corresponding reducible Verma module has a singular vector
at the level
This condition for the existence of a singular vector at the level
is not necessary. In particular, there is a singular vector at the level
. This singular vector is now a descendent of another singular vector at the level
. This type of singular vectors can however only exist if the central charge is of the type
coprime, these are the central charges of the minimal models
Hermitian form and unitarity
A highest weight representation with a real value of
has a unique Hermitian form such that the Hermitian adjoint of
and the norm of the primary state is one.The representation is called unitary
if that Hermitian form is positive definite. Since any singular vector has zero norm, all unitary highest weight representations are irreducible.
The Gram determinant of a basis of the level
is given by the Kac determinant formula
where the function p
) is the partition function
is a positive constant that does not depend on
. The Kac determinant formula was stated by V. Kac
(1978), and its first published proof was given by Feigin and Fuks (1984).
The irreducible highest weight representation with values and is unitary if and only if either ≥ 1 and ≥ 0, or
is one of the values
= 1, 2, 3, ..., m
− 1 and s
= 1, 2, 3, ..., r
Daniel Friedan, Zongan Qiu, and Stephen Shenker (1984) showed that these conditions are necessary, and Peter Goddard, Adrian Kent, and David Olive (1986) used the coset construction or GKO construction (identifying unitary representations of the Virasoro algebra within tensor products of unitary representations of affine Kac–Moody algebras) to show that they are sufficient.
The character of a representation
of the Virasoro algebra is the function
} q^.The character of the Verma module
}(q) = \frac = \frac=q^\left(1+q+2q^2+3q^3+5q^4+\cdots\right), where
is the Dedekind eta function
, the Verma module
is reducible due to the existence of a singular vector at level
. This singular vector generates a submodule, which is isomorphic to the Verma module
. The quotient of
by this submodule is irreducible if
does not have other singular vectors, and its character is
} = \chi_ -\chi_ = (1-q^) \chi_.
is in the Kac table of the corresponding minimal model
). The Verma module
has infinitely many singular vectors, and is therefore reducible with infinitely many submodules. This Verma module has an irreducible quotient by its largest nontrivial submodule. (The spectrums of minimal models are built from such irreducible representations.) The character of the irreducible quotient is
}-\chi_\right).\endThis expression is an infinite sum because the submodules
have a nontrivial intersection, which is itself a complicated submodule.
Conformal field theory
In two dimensions, the algebra of local conformal transformations is made of two copies of the Witt algebra.It follows that the symmetry algebra of two-dimensional conformal field theory is the Virasoro algebra. Technically, the conformal bootstrap approach to two-dimensional CFT relies on Virasoro conformal blocks, special functions that include and generalize the characters of representations of the Virasoro algebra.
Since the Virasoro algebra comprises the generators of the conformal group of the worldsheet, the stress tensor in string theory obeys the commutation relations of (two copies of) the Virasoro algebra. This is because the conformal group decomposes into separate diffeomorphisms of the forward and back lightcones. Diffeomorphism invariance of the worldsheet implies additionally that the stress tensor vanishes. This is known as the Virasoro constraint, and in the quantum theory, cannot be applied to all the states in the theory, but rather only on the physical states (compare Gupta–Bleuler formalism).
Super Virasoro algebras
See main article: Super Virasoro algebra. There are two supersymmetric N = 1 extensions of the Virasoro algebra, called the Neveu–Schwarz algebra and the Ramond algebra. Their theory is similar to that of the Virasoro algebra, now involving Grassmann numbers. There are further extensions of these algebras with more supersymmetry, such as the N = 2 superconformal algebra.
See main article: W-algebra. W-algebras are associative algebras which contain the Virasoro algebra, and which play an important role in two-dimensional conformal field theory. Among W-algebras, the Virasoro algebra has the particularity of being a Lie algebra.
Affine Lie algebras
See main article: affine Lie algebra. The Virasoro algebra is a subalgebra of the universal enveloping algebra of any affine Lie algebra, as shown by the Sugawara construction. In this sense, affine Lie algebras are extensions of the Virasoro algebra.
Meromorphic vector fields on Riemann surfaces
The Virasoro algebra is a central extension of the Lie algebra of meromorphic vector fields with two poles on a genus 0 Riemann surface.On a higher-genus compact Riemann surface, the Lie algebra of meromorphic vector fields with two poles also has a central extension, which is a generalization of the Virasoro algebra. This can be further generalized to supermanifolds.
Vertex algebras and conformal algebras
The Virasoro algebra also has vertex algebraic and conformal algebraic counterparts, which basically come from arranging all the basis elements into generating series and working with single objects.
The Witt algebra (the Virasoro algebra without the central extension) was discovered by É. Cartan (1909). Its analogues over finite fields were studied by E. Witt in about the 1930s. The central extension of the Witt algebra that gives the Virasoro algebra was first found (in characteristic p > 0) by R. E. Block (1966, page 381) and independently rediscovered (in characteristic 0) by I. M. Gelfand and Dmitry Fuchs (1968). Virasoro (1970) wrote down some operators generating the Virasoro algebra (later known as the Virasoro operators) while studying dual resonance models, though he did not find the central extension. The central extension giving the Virasoro algebra was rediscovered in physics shortly after by J. H. Weis, according to Brower and Thorn (1971, footnote on page 167).
- . 1984 . Infinite conformal symmetry in two-dimensional quantum field theory . . 241 . 333–380 . 10.1016/0550-3213(84)90052-X . 2. 1984NuPhB.241..333B .
- R. E. Block . 1966 . On the Mills–Seligman axioms for Lie algebras of classical type . . 121 . 378–392 . 1994485 . 10.1090/S0002-9947-1966-0188356-3 . 2. free .
- R. C. Brower . C. B. Thorn . 1971 . Eliminating spurious states from the dual resonance model . . 31 . 1 . 163–182 . 10.1016/0550-3213(71)90452-4. 1971NuPhB..31..163B . .
- E. Cartan . 1909 . Les groupes de transformations continus, infinis, simples . Annales Scientifiques de l'École Normale Supérieure . 26 . 93–161 . 40.0193.02 . 10.24033/asens.603. free .
- B. L. Feigin, D. B. Fuchs, Verma modules over the Virasoro algebra L. D. Faddeev (ed.) A. A. Mal'tsev (ed.), Topology. Proc. Internat. Topol. Conf. Leningrad 1982, Lect. notes in math., 1060, Springer (1984) pp. 230–245
- Friedan, D., Qiu, Z. and Shenker, S. . 1984 . Conformal invariance, unitarity and critical exponents in two dimensions . . 52 . 1575–1578 . 10.1103/PhysRevLett.52.1575 . 18. 1984PhRvL..52.1575F . 122320349 . .
- I.M. Gel'fand, D. B. Fuchs, The cohomology of the Lie algebra of vector fields in a circle Funct. Anal. Appl., 2 (1968) pp. 342–343 Funkts. Anal. i Prilozh., 2 : 4 (1968) pp. 92–93
- P. Goddard, A. Kent . D. Olive . amp . 1986 . Unitary representations of the Virasoro and super-Virasoro algebras . . 103 . 1 . 105–119 . 0826859 . 0588.17014 . 10.1007/BF01464283. 1986CMaPh.103..105G . 91181508 . .
- A. Kent . 1991 . Singular vectors of the Virasoro algebra . . 273 . 1–2 . 56–62 . 10.1016/0370-2693(91)90553-3. hep-th/9204097 . 1991PhLB..273...56K . 15105921 .
- V. G. Kac, "Highest weight representations of infinite dimensional Lie algebras", Proc. Internat. Congress Mathematicians (Helsinki, 1978), pp.299-304
- V. G. Kac, A. K. Raina, Bombay lectures on highest weight representations, World Sci. (1987) .
- Dobrev . V. K. . 1986 . Multiplet classification of the indecomposable highest weight modules over the Neveu-Schwarz and Ramond superalgebras . Lett. Math. Phys. . 11 . 3. 225–234 . 10.1007/bf00400220 . 1986LMaPh..11..225D. 122201087 . & correction: ibid. 13 (1987) 260.
- V. K. Dobrev, "Characters of the irreducible highest weight modules over the Virasoro and super-Virasoro algebras", Suppl. Rendiconti del Circolo Matematico di Palermo, Serie II, Numero 14 (1987) 25-42.
- Antony Wassermann. Lecture notes on Kac-Moody and Virasoro algebras . 1004.1287. math.RT. 2010. Antony Wassermann .
- Antony Wassermann. Direct proofs of the Feigin-Fuchs character formula for unitary representations of the Virasoro algebra. 1012.6003. 2010. math.RT. Antony Wassermann.
Notes and References
- M. A. Virasoro . 1970 . Subsidiary conditions and ghosts in dual-resonance models . . 1 . 10 . 2933–2936. 10.1103/PhysRevD.1.2933. 1970PhRvD...1.2933V .
- 10.1007/BF01218387 . A presentation for the Virasoro and super-Virasoro algebras . Communications in Mathematical Physics. 117 . 4 . 595 . 1988. Fairlie . D. B. . Nuyts . J. . Zachos . C. K. . 1988CMaPh.117..595F . 119811901 .
- 10.1007/BF01221412 . Redundancy of conditions for a Virasoro algebra . Communications in Mathematical Physics . 122 . 1 . 171–173 . 1989 . Uretsky . J. L. . 1989CMaPh.122..171U . 119887710 .
- P. Di Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory, 1997, .
- Krichever . I. M. . Novikov . S.P. . 1987 . Algebras of Virasoro type, Riemann surfaces and structures of the theory of solitons . Funkts. Anal. Appl. . 21 . 2. 46–63 . 10.1007/BF01078026 . 55989582 .
- 10.1016/0393-0440(94)00012-S. Super elliptic curves. Journal of Geometry and Physics. 15. 3. 252–280. 1995. Rabin . J. M. . hep-th/9302105 . 1995JGP....15..252R . 10921054.
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Area of Triangles
Let’s use what we know about parallelograms to find the area of triangles.
8.1: Composing Parallelograms
Here is Triangle M.
Han made a copy of Triangle M and composed three different parallelograms using the original M and the copy, as shown here.
For each parallelogram Han composed, identify a base and a corresponding height, and write the measurements on the drawing.
- Find the area of each parallelogram Han composed. Show your reasoning.
8.2: More Triangles
Find the areas of at least two of these triangles. Show your reasoning.
8.3: Decomposing a Parallelogram
Your teacher will give you two copies of a parallelogram. Glue or tape one copy of your parallelogram here and find its area. Show your reasoning.
Decompose the second copy of your parallelogram by cutting along the dotted lines. Take only the small triangle and the trapezoid, and rearrange these two pieces into a different parallelogram. Glue or tape the newly composed parallelogram on your paper.
- Find the area of the new parallelogram you composed. Show your reasoning.
- What do you notice about the relationship between the area of this new parallelogram and the original one?
- How do you think the area of the large triangle compares to that of the new parallelogram: Is it larger, the same, or smaller? Why is that?
Glue or tape the remaining large triangle to your paper. Use any part of your work to help you find its area. Show your reasoning.
Can you decompose this triangle and rearrange its parts to form a rectangle? Describe how it could be done.
We can reason about the area of a triangle by using what we know about parallelograms. Here are three general ways to do this:
Make a copy of the triangle and join the original and the copy along an edge to create a parallelogram. Because the two triangles have the same area, one copy of the triangle has half the area of that parallelogram.
The area of Parallelogram B is 16 square units because the base is 8 units and the height 2 units. The area of Triangle A is half of that, which is 8 square units. The area of Parallelogram D is 24 square units because the base is 4 units and the height 6 units. The area of Triangle C is half of that, which is 12 square units.
Decompose the triangle into smaller pieces and compose them into a parallelogram.
In the new parallelogram, \(b = 6\), \(h = 2\), and \(6 \boldcdot 2 = 12\), so its area is 12 square units. Because the original triangle and the parallelogram are composed of the same parts, the area of the original triangle is also 12 square units.
Draw a rectangle around the triangle. Sometimes the triangle has half of the area of the rectangle.
The large rectangle can be decomposed into smaller rectangles. The one on the left has area \(4 \boldcdot 3\) or 12 square units; the one on the right has area \(2 \boldcdot 3\) or 6 square units. The large triangle is also decomposed into two right triangles. Each of the right triangles is half of a smaller rectangle, so their areas are 6 square units and 3 square units. The large triangle has area 9 square units.
Sometimes, the triangle is half of what is left of the rectangle after removing two copies of the smaller right triangles.
The right triangles being removed can be composed into a small rectangle with area \((2 \boldcdot 3)\) square units. What is left is a parallelogram with area \(5 \boldcdot 3 - 2 \boldcdot 3\), which equals \(15-6\) or 9 square units. Notice that we can compose the same parallelogram with two copies of the original triangle! The original triangle is half of the parallelogram, so its area is \( \frac12 \boldcdot 9\) or 4.5 square units.
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In simple words, we can say that the amount of time that has passed between the beginning and the end of an event is called the elapsed time. We can determine this time by subtracting the end time and the start time. The formula to calculate the elapsed time is simply to subtract the hours and minutes separately.
What is the formula of time in physics?
To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.
How do you find time change in physics?
How do you calculate elapsed time with speed?
What does elapsed time mean in physics?
Elapsed time is the amount of time that has passed during an event. Elapsed time can easily be calculated using a number line to determine the hours and minutes that have passed.
What is the elapsed time?
Elapsed time is the time or difference between a beginning time and an ending time. Finding elapsed time is an important skill in everyday life.
What are the 3 formulas in physics?
The three equations are, v = u + at. v² = u² + 2as. s = ut + ½at²
What are the formulas in physics?
- a = \fracv-ut
- \rho = \fracmV
- P= \fracWt
- P= \fracFA
- E = \frac12mv^2.
- f= \fracV\lambda
How do you find time in projectile motion physics?
T tof = 2 ( v 0 sin θ 0 ) g . T tof = 2 ( v 0 sin θ 0 ) g . This is the time of flight for a projectile both launched and impacting on a flat horizontal surface.
What is the formula for time in acceleration?
Acceleration (a) is the change in velocity (Δv) over the change in time (Δt), represented by the equation a = Δv/Δt. This allows you to measure how fast velocity changes in meters per second squared (m/s^2). Acceleration is also a vector quantity, so it includes both magnitude and direction. Created by Sal Khan.
How do you calculate motion in physics?
Newton’s second law, which states that the force F acting on a body is equal to the mass m of the body multiplied by the acceleration a of its centre of mass, F = ma, is the basic equation of motion in classical mechanics.
How do you calculate time given initial and final velocity and distance?
How do we find the elapsed time in minutes and seconds?
What is actual elapsed time example?
A schedule defined from 9am to 5pm is 8 hours long. If a task SLA starts at 12am, and the current time is 12pm, then the actual elapsed time is 12 hours, but the business elapsed time is 5 hours, and the business elapsed time will only restart at 9am on the following day.
How do you solve elapsed time word problems?
What is the elapsed time between 5.45 am and 4.10 pm?
The elapsed time between 5:45am and 4:10 pm is 10hours and 25 minutes.
How do you calculate elapsed time for a third grader?
Whats the elapsed time between 3 40am and 2 00pm?
What is the elapsed time between 3 40 AM and 2 00 PM? 10 hours and 20 minutes.
How do you find the elapsed time on a number line?
Whats the elapsed time between 2 16am and 8/10 pm?
The elapsed time between 2:16 AM and 8:10 PM is 17 hours and 54 minutes.
Is physics easy or hard?
Students and researchers alike have long understood that physics is challenging. But only now have scientists managed to prove it. It turns out that one of the most common goals in physics—finding an equation that describes how a system changes over time—is defined as “hard” by computer theory.
Is physics a math?
While physicists rely heavily on math for calculations in their work, they don’t work towards a fundamental understanding of abstract mathematical ideas in the way that mathematicians do. Physicists “want answers, and the way they get answers is by doing computations,” says mathematician Tony Pantev.
How do you memorize physics formulas?
- Step 1 – Free Yourself from Stress. To learn anything, you need to de-stress yourself first.
- Step 2 – Try to Understand the Formula.
- Step 3 – Constantly Work On It.
- Step 4 – Stop Relying on your Formula Sheet.
How can I study physics?
How can I learn physics?
- Mastering the basics is necessary: One of the easiest ways of learning physics is to master the basic theories.
- Simplification is a Key Rule:
- Create Flashcards:
- Make Math Your Strength:
- A good tutor makes a BIG difference!
- Use diagrammatic representations to learn the concepts:
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How Do You Calculate Gravity On Earth
Fgrav = m*g where d represents the distance from the center of the object to the center of the earth. In the first equation above, g is referred to as the acceleration of gravity. Its value is 9.8 m/s2 on Earth. That is to say, the acceleration of gravity on the surface of the earth at sea level is 9.8 m/s2.
What Does Mg Stand For In Physics: The Ultimate Convenience
To him it feels as though hes got to pump up your ego at each turn. Youre able to rinse and reuse the Styrofoam cups which dont have a hole inside them. The very first is the fact that its far better to stand near the urinal.
If you decide to, paint the exterior of the bucket, what ever color you want utilizing the spray primer. If you locate a scrape in a high traffic area with several deer trails, it might be employed by multiple bucks, this is a great hot spot to hunt. The water falling from the top cup is made from positive and negative pieces which are all jumbled together.
Example 2 What Is The Tension In A Tightrope
Calculate the tension in the wire supporting the 70.0-kg tightrope walker shown in Figure 6.
Figure 6. The weight of a tightrope walker causes a wire to sag by 5.0 degrees. The system of interest here is the point in the wire at which the tightrope walker is standing.
As you can see in the figure, the wire is not perfectly horizontal , but is bent under the persons weight. Thus, the tension on either side of the person has an upward component that can support his weight. As usual, forces are vectors represented pictorially by arrows having the same directions as the forces and lengths proportional to their magnitudes. The system is the tightrope walker, and the only external forces acting on him are his weight w and the two tensions TL and TR , as illustrated. It is reasonable to neglect the weight of the wire itself. The net external force is zero since the system is stationary. A little trigonometry can now be used to find the tensions. One conclusion is possible at the outsetwe can see from part of the figure that the magnitudes of the tensions TL and TR must be equal. This is because there is no horizontal acceleration in the rope, and the only forces acting to the left and right are TL and TR. Thus, the magnitude of those forces must be equal so that they cancel each other out.
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Whispered What Does Mg Stand For In Physics Secrets
Problems are simple to misidentify, and at times a change which works well for a single problem makes another problem worse. The laws of physics are thought to be fundamental, although a lot of them refer to idealized or theoretical systems that arent easy to replicate in the actual world. The idea of measurement is often misunderstood as merely the assignment of a value, but its possible to assign a value in a sense that isnt a measurement with respect to the demands of additive conjoint measurement.
Retort stands are frequently used in the chemistry laboratory. On the other hand, the biggest thing to consider while implementing readability is to help it become clutter-free. Temperature abbreviations are employed in all sorts of writing.
What Is The Difference Between Mcg And Mg Measurement
Receiving a correct dosage is one of the five rights of medication administration, for both prescription and over-the-counter drugs 5. Two examples of units of measurement common in medicine are mcg and mg. Though they’re very similar, they’re two different units of measure, and not knowing the difference can result in serious consequences if they’re not read correctly.
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What Does Mg Stand For In Physics At A Glance
Each Practice Test contains ten to twelve High School Physics problems you can utilize to hone your abilities. A video camera is advised for large lecture classes. Miscellaneous This section features questions on the historical features of physics and focuses on your capacity to execute graphical analysis or utilize math to fix problems.
1 way to produce huge numbers or little fractions simpler to read, is to use unit prefixes. To put it differently, a stone must have a minimum velocity so as to bounce. Thus, the kind of structure might be important, especially in the event the home is an old one.
It is crucial to stay calm and attempt to bring the problem to a situation which youre acquainted with by simplifying it in your thoughts. The affair and the youngster should now be previously. Whatever happens, the youngster isnt at fault.
If you really on guys to produce your life go, then you should reexamine your life. If you like the person who you are with, you have to concentrate on such a love life. Look past how youll no longer need to deal with your wifes moodiness or anger.
Radon in well water can be published into the air of the house in the duration of various water-using pursuits. Acquiring exact measurements can help you determine the kind and volume of goods to bring. Although placing take a place together may seem to be an effective and effortless effort, this is nowhere near the instance.
Details Of What Does Mg Stand For In Physics
If you attempt to pressure or manipulate the scenario, it will probably backfire on you. Once you get your hole cut, you can slide your horse on the pole and choose at what point you wish to set your horse permanently. go to my site In the event the stand has a great deal of variability more points ought to be taken.
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The What Does Mg Stand For In Physics Pitfall
Failure hurts, but its often essential to experience failure in order to reach the best success. You ought to be knowledgeable about the different kinds of nuclear reactions and be in a position to explain several theories on relativity. For instance, a drug company might need to test a new cancer drug to learn if it improves life expectancy.
Cartoons Get a personalized cartoon commissioned for the rear of your card. As people, were unique characters. Say, as an example, a sign right outside the door of your store wont require an enormous font, whereas, in the event the banner is being put up on the face of the highway, the font size should be incremented substantially.
Used only whenever the term assortment is part of the item name. This abbreviation is use only whenever the term outfit is part of the item name. It is used only when the term strip is a part of the item name.
Type Of What Does Mg Stand For In Physics
There are a few genuine nice features to get on your table and some you may not require. There is, in addition, the element of distractions. A pure standing wave is going to have an infinite SWR.
As soon as you find these areas this is the location where you want to produce your mock scrape. By positioning your head correctly, it is going to be over the water and youd be in a position to breathe. Never wait over 30 minutes for him again.
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Theres no need to bring a s to an abbreviation to demonstrate a plural. An abbreviation may be formed utilizing the initial and last letter of the whole word. It is used only when the term strip is a part of the item name.
What Is The Si Unit
SI unit is an international system of measurements that are used universally in technical and scientific research to avoid the confusion with the units. Having a standard unit system is important because it helps the entire world to understand the measurements in one set of unit system. Following is the table with base SI units:
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When Does Normal Force Equal To $mg$
Can someone once and for all explain when does normal force equal to mg?
I know for sure that when there is no friction, normal force will be equal to mg.But, i encountered some questions when there is some mass on an incline with friction, and then the normal force was the y component of mg.
It does not make sense to me, because as i understood when there is friction, we cannot assume that mg will be equal to normal force.
Normal Force arises due to the Newtons Third law. Normal Force will be always acting opposite to the force falling on the surface.Normal Force is a reaction force. Remember
Normal force is equal to mg only when the object is placed horizontally, and the force is acting in the direction of the gravitational field.
Now your second question
Here you will see that the weight of the body is passing through the Centre of gravity and acting in direction of the centre of the earth.
But the component of weight on the incline is not mg it is cos component.In order to satisfy the Newtons third law Normal reaction to the object is the cos component$$N=Wg\cos \theta$$ even if friction is there or not there this will be the same
Normal force $F_N$ is just the force between two surfaces. Its called normal because it acts perpendicular to the surfaces.
Gravitational force is completely unrelated. Gravity always acts with $F_g = -mg$. The minus sign indicates that the force points down.
What Does Mg Stand For In Physics Explained
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The Air Resistance Force
To keep our discussion under control, we will restrict our discussion to air resistance forces proportional to v and v2.
Many sources attempt to treat all of the non-velocity influences on the drag force separately. So, we have a constant/variable that represents the influence of the shape of the object on the air resistance force, a constant/variable that represents effect of the density of the fluid on the air resistance force, etc. This results in a very large, very complicated looking expression for the air resistance force. If your life isn’t complicated enough, I recommend that you switch to one of these treatments. My choice is to lump all of these other factors into one constant – let’s call it “b”. So, the shape of the object influences the value of “b”, the density of the fluid influences “b”, and so on.
This means that we can write the air resistance force as fdrag = bv for very small, slow objects, or fdrag = bv2 for “human-size objects, depending on the situation.
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Static Friction And Kinetic Friction
Recall from the previous chapter that friction is a force that opposes motion, and is around us all the time. Friction allows us to move, which you have discovered if you have ever tried to walk on ice.
There are different types of frictionâkinetic and static. Kinetic friction acts on an object in motion, while static friction acts on an object or system at rest. The maximum static friction is usually greater than the kinetic friction between the objects.
Example 1 Weight On An Incline A Two
Consider the skier on a slope shown in Figure 2. Her mass including equipment is 60.0 kg. What is her acceleration if friction is negligible? What is her acceleration if friction is known to be 45.0 N?
Figure 2. Since motion and friction are parallel to the slope, it is most convenient to project all forces onto a coordinate system where one axis is parallel to the slope and the other is perpendicular . N is perpendicular to the slope and f is parallel to the slope, but w has components along both axes, namely w and \textbf_. N is equal in magnitude to w, so that there is no motion perpendicular to the slope, but f is less than w, so that there is a downslope acceleration .
The magnitude of the component of the weight parallel to the slope is _= \sin = mg\sin , and the magnitude of the component of the weight perpendicular to the slope is _=\cos = mg\cos.
Neglecting friction. Since the acceleration is parallel to the slope, we need only consider forces parallel to the slope. The forces parallel to the slope are the amount of the skiers weight parallel to the slope w and friction f. Using Newtons second law, with subscripts to denote quantities parallel to the slope,
where _\parallel}=_=mg\sin, assuming no friction for this part, so that
is the acceleration.
and substituting this into Newtons second law, _=\frac_\parallel }}, gives
We substitute known values to obtain
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What Does Fg Mean In Food & Nutrition
This page is about the meanings of the acronym/abbreviation/shorthand FG in the Miscellaneous field in general and in the Food & Nutrition terminology in particular.
Find a translation for Food Grade in other languages:
Select another language:
What does FG mean?
- Fg is an abbreviation used in physics and engineering for the force exerted by gravity on an object, normally represented in units such as the newton. Fg is always a conservative force.
F = Ma Also Equals To F = Mg F = Fa
Answer: Constant speed => a = 0
F = ma = 0
F = Fa – Ff
Ff – Fa = 50N
EDIT: I’m sorry, mistook the equal for a minus. So is the equation correct now?
Hi, Why is F = ma equals to F =mg?
Also what is F = Fa – Ff? It came from this question.The question is c) If the box moves at a constant speed of 2m/s-1 when a 50N force is applied, what is the frictional force? Answer: Constant speed => a = 0F = ma = 0F = Fa – Ff Ff = Fa = 50N
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Objects Fall At The Same Rate
The most outstanding characteristic of gravity is the fact that all objects fall at the same rateassuming the effect of air resistance is negligible. This is because the acceleration due to gravity, g, is a constant for all objects, no matter what their mass.
This seems counterintuitive, since you would expect a heavy object to fall faster than an object that weighed less. But it is a fact. Try dropping two objects at the same time, from the same height, making sure they are heavy enough not to be affected by air resistance. You will see they hit the ground at the same time.
A Secret Weapon For What Does Mg Stand For In Physics
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- Let’s see how the surface area and volume of solids change when we dilate them.
6.1: Math Talk: Cube Volumes
Find the volume of each cube mentally.
6.2: How Do Surface Area and Volume Change with Scaling?
- Use the applet to build cubes that result from dilating a unit cube by each scale factor shown in the table. Then, complete the table with the surface area and volume of each dilated cube.
scale factor surface area in square units volume in cubic units 1 2 3 4
- Suppose a unit cube is dilated by some scale factor \(k\).
- Write an expression for the surface area of the dilated cube.
- Write an expression for the volume of the dilated cube.
- Compare and contrast the expression for surface area and the expression for volume.
6.3: Scaling All Solids
Clare says, “We know that if we dilate a cube by a factor of \(k\), the cube’s volume is multiplied by \(k^3\). It seems like that must apply to all solids, but I’m not sure how to prove it.”
Elena says, “Earlier in the unit, we showed that we can cover any two-dimensional shape with rectangles, so the property that area changes by \(k^2\) when we dilate a figure by \(k\) applies to all shapes, not just rectangles. Can we do something similar here?”
- Use Elena’s line of reasoning to argue that for any solid, if it’s dilated by a factor of \(k\), the volume is multiplied by \(k^3\).
- Suppose a triangular prism has surface area 84 square centimeters and volume 36 cubic centimeters. The prism is dilated by scale factor \(k=4\). Calculate the surface area and volume of the dilated prism.
The image shows a figure called Sierpinski’s triangle. It’s formed by starting with an equilateral triangle, then repeatedly removing equilateral triangles created by joining the midpoints of the existing triangle’s sides. The first few stages are shown.
If we continue this process of removal forever, we are left with some points that never get removed from the triangle. The remaining points are what we call Sierpinski’s triangle. At any given stage, the triangle at the top of the figure is a scaled copy of the triangle at the previous stage.
For the completed Sierpinski’s triangle, though, the top triangle is a scaled copy not of the previous stage, but of the full Sierpinski’s triangle.
- For the completed figure, what scale factor takes Sierpinski’s triangle to its scaled copy at the top?
- Based on the scale factor, what fraction of the original shaded region should be contained in the scaled copy at the top?
- The scaled copy at the top actually contains \(\frac13\) of the shading of the original. Provide reasoning that shows that this is true.
In earlier activities, we saw that if we dilate a two-dimensional shape, the area of the dilated shape is the area of the original shape multiplied by the square of the scale factor. What happens when we dilate three-dimensional solids?
Here is a rectangular prism with side lengths 3, 4, and 5 units. When we dilate the prism using a scale factor of 3, the lengths become 9, 12, and 15 units.
Since these are three-dimensional shapes, we can look at both volume and surface area. The volume of the original prism is 60 cubic units because \(3 \boldcdot 4 \boldcdot 5=60\). The volume of the dilated prism is 1,620 cubic units because \(9 \boldcdot 12 \boldcdot 15=1,\!620\). The volume became 27 times larger! Why? Since the side lengths tripled, when we calculated the volume we were really finding \((3 \boldcdot 3) \boldcdot (4 \boldcdot 3) \boldcdot (5 \boldcdot 3) = (3 \boldcdot 4 \boldcdot 5)\boldcdot 3^3\). The volume was multiplied by the cube of the scale factor, or by \(3^3=27\).
Now let’s look at surface area. How do you think the surface area will change when the prism is dilated?
In the original prism, 2 faces have area 12 square units, 2 have area 20 square units, and 2 have area 15 square units for a total surface area of 94 square units. The corresponding faces of the dilated prism have areas 108, 180, and 135 square units. The surface area of the new prism totals 846 square units, 9 times that of the original. Just like the area of two-dimensional shapes, the surface area of the prism changed by the square of the scale factor.
In general, when you dilate any three-dimensional solid by scale factor \(k\), the surface area is multiplied by \(k^2\) and the volume is multiplied by \(k^3\).
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Increasing and Decreasing
Let’s use percentages to describe increases and decreases.
3.1: Improving Their Game
Here are the scores from 3 different sports teams from their last 2 games.
|sports team||total points in game 1||total points in game 2|
- What do you notice about the teams’ scores? What do you wonder?
- Which team improved the most? Explain your reasoning.
3.2: More Cereal and a Discounted Shirt
A cereal box says that now it contains 20% more. Originally, it came with 18.5 ounces of cereal. How much cereal does the box come with now?
The price of a shirt is \$18.50, but you have a coupon that lowers the price by 20%. What is the price of the shirt after using the coupon?
3.3: Using Tape Diagrams
Match each situation to a diagram. Be prepared to explain your reasoning.
- Compared with last year’s strawberry harvest, this year’s strawberry harvest is a 25% increase.
- This year’s blueberry harvest is 75% of last year’s.
- Compared with last year, this year’s peach harvest decreased 25%.
- This year’s plum harvest is 125% of last year’s plum harvest.
Draw a diagram to represent these situations.
The number of ducks living at the pond increased by 40%.
- The number of mosquitoes decreased by 80%.
What could it mean to say there is a 100% decrease in a quantity? Give an example of a quantity where this makes sense.
3.4: Agree or Disagree: Percentages
Do you agree or disagree with each statement? Explain your reasoning.
Employee A gets a pay raise of 50%. Employee B gets a pay raise of 45%. So Employee A gets the bigger pay raise.
- Shirts are on sale for 20% off. You buy two of them. As you pay, the cashier says, “20% off of each shirt means 40% off of the total price.”
Imagine that it takes Andre \(\frac34\) more than the time it takes Jada to get to school. Then we know that Andre’s time is \(1\frac34\) or 1.75 times Jada’s time. We can also describe this in terms of percentages:
We say that Andre’s time is 75% more than Jada’s time. We can also see that Andre’s time is 175% of Jada’s time. In general, the terms percent increase and percent decrease describe an increase or decrease in a quantity as a percentage of the starting amount.
For example, if there were 500 grams of cereal in the original package, then “20% more” means that 20% of 500 grams has been added to the initial amount, \(500+(0.2)\boldcdot 500=600\), so there are 600 grams of cereal in the new package.
We can see that the new amount is 120% of the initial amount because
\(\displaystyle 500+(0.2)\boldcdot 500 = (1 + 0.2)500\)
- percentage decrease
A percentage decrease tells how much a quantity went down, expressed as a percentage of the starting amount.
For example, a store had 64 hats in stock on Friday. They had 48 hats left on Saturday. The amount went down by 16.
This was a 25% decrease, because 16 is 25% of 64.
- percentage increase
A percentage increase tell how much a quantity went up, expressed as a percentage of the starting amount.
For example, Elena had $50 in the bank on Monday. She had $56 on Tuesday. The amount went up by $6.
This was a 12% increase, because 6 is 12% of 50.
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Module 3: LaTeX on Various Platforms
The learning goals for this module include:
- Learn about the LaTeX support provided by environments like GeoGebra, Brightspace, and Google Docs.
- Explore other platforms that offer LaTeX support.
Before You Start
Think of a few different document types or platforms that you use to communicate mathematics. This might include word-processors, slide-presentation software, online learning environments, webpages, graphing calculators, etc. How many different tools do you need to use to insert mathematical expressions and symbols into these environments?
The LaTeX support included in various digital platforms allows you to use LaTeX or LaTeX-style commands to include mathematics without having to create an entire LaTeX document. In most chases, there are facilities on these platforms to inject a small amount of LaTeX (just what you need) into your document or page.
LaTeX in GeoGebra
The free online graphing and geometry tool GeoGebra includes LaTeX support in its text tool, allowing you to include LaTeX-based formulas on graphs and sketches that you create.
Try out the GeoGebra support for LaTeX following these steps:
- Go to the GeoGebra graphing calculator page.
- Select the Tools menu and choose the Text Tool within the Media Tools category.
- Click on the graphing area to bring up the Text Tool, and select LaTeX Formula.
- Enter one of the LaTeX commands you have learned.
Read more about GeoGebra's LaTeX support on the GeoGebra wiki.
LaTeX in Brightspace
The virtual learning environment Brightspace has a LaTeX editor that is similar to the GeoGebra editor and the simple LaTeX renderer included in this course.
- In any Brightspace text editor, click on the "Show All Components" button (the ellipsis ...)
- Clicking on the Sigma button will show a dropdown with options for equation and symbol insertion.
- You can choose the LaTeX editor from the list.
LaTeX in Google Docs
Google Docs allows you to insert equations into your documents, and provides an equation editor to help you create the mathematics you want. However, if you know a bit of LaTeX, you can speed things up by using the Google Docs Equation Shortcuts, which are essentially LaTeX commands without the curly braces.
Google's official documentation on the use of equation shortcuts is very brief, but one enterprising user has come up with an unofficial cheatsheet.
Once you have finished typing the shortcut, Google Docs will automatically replace it with the symbol, and create editable spaces for you to put any required arguments. For example, typing "\frac" within the equation editing region will cause Google Docs to create a horizontal line, and places for the numerator and denominator.
If you have a Google account, try following these steps:
- Open a new Google Doc file.
- From the Insert menu, select Equation.
- In the text area created, type a simple command, like "\alpha" followed by a space.
- Note that your command should be replaced by an appropriate symbol.
LaTeX on any Web Page
The MathJax provides instructions on how to include MathJax on any webpage you author. As described there, including a small script will allow you to insert LaTeX formatted math using delimiters: backslashes with round brackets for inline math, and backslashes with square brackets for displayed equations.
This method can be used on some web-page authoring and blogging platforms that do not offer explicit LaTeX support. If there is a facility for inserting a script, you can insert the MathJax code, and start using LaTeX on your page. This is one way to get LaTeX support on Blogger-based blogs, for example.
MathJax offers support for advanced LaTeX formatting and configuration - please see their docs for more information.
LaTeX in Other Documents
If you are creating a document in another platform that does not have LaTeX support, you can use online LaTeX editors and insert the displayed math as an image file into your document. As described in module 1, editors like CodeCogs, or QuickLaTeX allow you to download a rendered image of your LaTeX commands. Alternatively, you could use the simple LaTeX renderer here and use a screen-capture tool to obtain an image of your equation.
Malin Christersson has a nice page about LaTeX on the web, which includes some background, brief descriptions of Wikipedia, Wordpress, and various wiki-engine support for LaTeX, and a short overview of MathJax.
The popular graphing calculator Desmos will automatically render the math you type correctly. But did you know that it uses LaTeX behind the scenes (via another software library, MathQuill), and can even act like a LaTeX editor? In Desmos, type any equation, like "y=sin(theta)", highlight what you typed and copy it into a plain text editor. You will see that the result is a set of LaTeX commands that give the typed math that you see in Desmos. This suggest that if you want to get a bit of LaTeX code but you don't know the commands, you can type it in Desmos and copy the commands from there.
Before moving on to the next module, take a moment to review the learning checklist.
If there were any items in the checklist that you did not complete, consider reviewing this page again before moving on.
Christersson. M. (2019). LaTeX on the Web. webpage. Retrieved March 7, 2019 from http://www.malinc.se/math/latex/latexontheweben.php
D2L Corporation. (2019). Brightspace Learning Platform. Retrieved on March 18, 2019 from https://www.d2l.com/
Desmos Inc. (2019). Desmos Graphing Calculator. Software. Retrieved on March 18, 2019 from https://www.desmos.com/
GeoGebra Group. (2018). GeoGebra Online Math Applications. Retrieved on March 18, 2019 from https://www.geogebra.org/?lang=enGeoGebra Group. (2018). LaTeX in GeoGebra. Retrieved on March 18, 2019 https://wiki.geogebra.org/en/LaTeX
Google Corp. (2019). Google Docs, G-Suite Application, https://www.google.com/docs/about/
Notuom.com (2017). Google Docs Equation Editor Unofficial Shortcuts List / Cheat Sheet. Retrieved on March 19, 2019 from http://www.notuom.com/google-docs-equation-shortcuts.html
Overleaf Inc. (2019). Overleaf Cloud-based LaTeX Document Preparation Software. Retrieved on March 18, 2019 from https://www.overleaf.com/about
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