- #1

- 95

- 0

Is angular kinetic energy also conserved with angular momentum?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

In summary, the conversation discusses the conservation of angular momentum and the relationship between angular kinetic energy and angular momentum. It is noted that while angular momentum is conserved, angular kinetic energy is not due to the work of internal forces in the system. The concept of rotational energy is also briefly mentioned. A discussion then ensues about the representation of energy as a vector and how it relates to the conservation of energy in a closed system.

- #1

- 95

- 0

Is angular kinetic energy also conserved with angular momentum?

Physics news on Phys.org

- #2

Angular momentum is conserved because of the absence of external torques.

- #3

- 322

- 0

- #4

btw. seeing linear momentum is mv. KE = 1/2mv^2. Is it just coincidence that KE is antiderivative of momentum or is it supposed to be that way. I've noted this a few times but I've never had a professor get up and say "Kinetic energy is the antiderivative of momentum" so i was just wondering.

- #5

- 95

- 0

I guess I just don't understand how that work done pulling the weights closer to you would go twords increasing KE.

Would anyone mind laying out the problem and solving?

It just doesn't make sense that momentum can stay the same while energy changes.

Would anyone mind laying out the problem and solving?

It just doesn't make sense that momentum can stay the same while energy changes.

Last edited:

- #6

Originally posted by Rockazella

Would anyone mind laying out the problem and solving?

It just doesn't make sense that momentum can stay the same while energy changes.

Well it makes sense according to classical physics, but if you don't like it you can make your own... you must just be self-consistent and convince a few others ;)

Besides teasing you, Let us put down a very symple system that will show you how the whole thing works.

Something like two point-like masses hold together by a spring, rotating around an axis orthogonal to the spring with constant angular velocity. If the spring is initially extended beyong its rest length and kept so by a thin rod, we will have a system where we can easily describe the internal forces by a potential energy. If at some point the thin rod breaks, total energy will be conserved (no other force is involved in the system besides the conservative elastic one); since that time on the evolution of the system is dictated by conservation of angular momentum (no external momentum of force is present) and of total energy. While the two masses are coming together there is an increase of angular velocity which implies an increse of kinetic energy which is compensated (to keep total energy constant) by a reduction of potential energy. During the expansion the opposite happens.

In the case of a human bringing two weights closer it is the chemical energy stored in some molecules that is converted to kinetic energy (and to heat), while conserving angular momentum.

- #7

there is only one energy which is vector product of the force vector and the so called X vector.this X vector is actually the distance of the point where the force is acting and the equilibrum point(the point where the force virtually reduce to zero).important is that the energy defined as above is always constant if the system is closed.

i din't tought/comment of/on your wonder here but give me some finite time and i'll come up with something.

- #8

- 95

- 0

Thanks dg, I think it just clicked in my mind. It's starting to make more sense now.

- #9

there is only one energy in the system and it is E=FxX=const

X is equilibrum vector starting in the position of the weight and ending in the normal projection of the same position on the axis of rotation.Now the explanation is simple as A,B,C...

pulling the weight closer to the axis of rotation declines X but since FxX=E=const increases F.X is normal to the trajectory of the weight and F is parallel(tangential).But it also has to be FxdX=F'xdX'

left are the old values and right are the new values.that's why the tangential displacement is larger closer to the axis of rotation.

when you increase X then F drops and dX (the old)> dX' (the new ).

The only thing conserved here is the energy.

I don't know about the momentum cause at the moment like everything else in physics I'm considering time being vector.

- #10

Science Advisor

- 1,479

- 26

Originally posted by dock

there is only one energy which is vector product of the force vector and the so called X vector.this X vector is actually the distance of the point where the force is acting and the equilibrum point(the point where the force virtually reduce to zero).important is that the energy defined as above is always constant if the system is closed.

i din't tought/comment of/on your wonder here but give me some finite time and i'll come up with something.

I'm curious to know how energy can be represented as a vector

- #11

here is how:Originally posted by Claude Bile

I'm curious to know how energy can be represented as a vector

assume you have an weight hanging on a spring in equilibrium point. then the resulting force is zero thus no movement. now pull the weight down displacing it for some X value. now the resulting force is again zero but when you release the weight the active force is same as but oposite with the one you have invested to cause the initial displacement. there are two scenarios availabe to consider:

(1st scenario) assuming that at the moment you release the weight the action force is Fmax. in that moment the weight is in equilibrium point and the equilibrium distance is zero. the action force is causing displacement in same direction of the the force cause the job done by the action force is always positive. as you increase the equilibrium distance you decline the force.when the force reduces to zero then the equlibrium distance is maximum. the force onwards change the sing and becomes negative therefore and the equilibrium distance does the same too. when the force reaches value -Fmax the the equilibrium distance drops to zero and so on. simbolically it looks like this:

(1 moment)F=Fmax and X=0

(2 moment)F>0 and F->0 and X > 0 and X->Xmax

(3 moment)F<0 and F->0 and X < 0 and X->-Xmax

(4 moment)F=-Fmax and X=0

(5 moment)F<0 and F->0 and X < 0 and X->-Xmax

(6 moment)F>0 and F->0 and X > 0 and X->Xmax

(7 moment)same as moment 1 and everything from the begining

thusF=Fmax * cos(fi1) and X=Xmax * sin(fi1)

(2nd scenario)the second scenario is when you assume that at the moment of release of the weight X=Xmax then simbolically it looks like this:

(1 moment)X=Xmax and F=0

(2 moment)X>0 and X->0 and F > 0 and F->Fmax

(3 moment)X<0 and X->0 and F < 0 and F->-Fmax

(4 moment)X=-Xmax and F=0

(5 moment)X<0 and X->0 and F < 0 and F->-Fmax

(6 moment)X>0 and X->0 and F > 0 and F->Fmax

(7 moment)same as moment 1 and everything from the begining

thusX=Xmax * cos(-fi1) and F=Fmax * sin(-fi1)

what i have found is that both scenarios are corect and that they are only the same story from different aspect. the first nlue tush is for the x coordinates and the 2nd tush are the y coordinates while the z coordinates both for X and F are zeros. but therefore the x and y coordinates of energy are zeros too.the z coordinate of energy then will be

E(x)=Fmax * sin(-fi1)*0+Xmax * sin(fi1)*0=0

E(y)=Fmax * cos(fi1)*0+Xmax * sin(-fi1)*0=0

E(z)=Fmax * cos(fi1)Xmax * cos(-fi1)-Fmax * sin(-fi1)Xmax * cos(-fi1)

E(z)=Fmax*Xmax*(cos^2(fi1)+sin^2(fi1))=Fmax*Xmax

this equation comes from vector procut of two vectors.in the end i conclude that energy is actually a vector product of force vector and the equilibrium vector.

STICK WITH ME YOU'LL LEARN MUCH MORE!

- #12

- 333

- 1

Not every system can have the 'point of equilibrum' that you are defining.Originally posted by dock

actually there is no such thing as Kinetic Energy or Potential Energy.

there is only one energy which is vector product of the force vector and the so called X vector.this X vector is actually the distance of the point where the force is acting and the equilibrum point(the point where the force virtually reduce to zero).important is that the energy defined as above is always constant if the system is closed. i din't tought/comment of/on your wonder here but give me some finite time and i'll come up with something. [/B]

Take for example, a guy is sliding a box on a rough surface, where is the point of equilibrum ?

But we can say that all the laws (as far as i know so far) of energy can be derived from the definition of Work.

Last edited:

- #13

if you know the energy vector and the force vector then sinceOriginally posted by STAii

Not every system can have the 'point of equilibrum' that you are defining.

Take for example, a guy is sliding a box on a rough surface, where is the point of equilibrum ?

But we can say that all the laws (as far as i know so far) of energy can be derived from the definition of Work.

E=FxX => Fx(ExF)=Fx(X) => X=ExF

where X is the equilibrium vector.

hey energy being vector is new to me too.

redirecting...:

https://www.physicsforums.com/showthread.php?s=&threadid=1000

find out more of Kinetic Energy.

Angular kinetic energy is the energy an object possesses due to its rotation. It is dependent on both the mass and the angular velocity of the object.

The formula for calculating angular kinetic energy is KE = 1/2 * I * ω^2, where KE is the angular kinetic energy, I is the moment of inertia, and ω is the angular velocity.

Angular kinetic energy and linear kinetic energy are related through the moment of inertia. The moment of inertia for a rotating object is equal to the mass of the object multiplied by the square of its distance from the axis of rotation. This means that an object with a higher moment of inertia will have a higher angular kinetic energy, but the linear kinetic energy will remain the same.

Angular kinetic energy does not directly affect an object's momentum. However, changes in angular kinetic energy can result in changes in angular momentum, which is a vector quantity that represents the rotational motion of an object.

Angular kinetic energy is applied in many real-world situations, such as in the motion of rotating objects like a spinning top or a bicycle wheel. It is also used in industries such as aerospace, where understanding the angular kinetic energy of rotating parts is crucial for safe and efficient operation.

Share:

- Replies
- 5

- Views
- 563

- Replies
- 3

- Views
- 860

- Replies
- 8

- Views
- 1K

- Replies
- 3

- Views
- 720

- Replies
- 9

- Views
- 961

- Replies
- 9

- Views
- 1K

- Replies
- 2

- Views
- 630

- Replies
- 2

- Views
- 685

- Replies
- 14

- Views
- 893

- Replies
- 9

- Views
- 1K