Conservation of Kenetic Energy: Rotational Style

In summary, the physics engine has a simple formula to deal with collisions. Momentum and Kinetic Energy have to be conserved, so m1v1 + m2v2 = m1u1 + m2u2. This can be solved for u1 and u2 (final velocities of each object) like this: u1 = (m1-m2)/(m1+m2)v1 + (m2+m2)/(m1+m2)v2, and u2 = (m1+m1)/(m1+m2)v1 + (m2-m1)/(m1+m2)v2.
  • #1
_Nate_
20
0
For my physics engine, I have a pretty simple formula to deal with collisions.

Essentially, in a collision, both Momentum and Kinetic Energy have to be conserved. Thus, m1v1 + m2v2 = m1u1 + m2u2 and m1v1^2 + m2v2^2 = m1u1^2 + m2u2^2, and, given m1, m2, v1, and v2, we can solve for u1 and u2 (final velocities of each object) like this:

u1 = (m1-m2)/(m1+m2)v1 + (m2+m2)/(m1+m2)v2
u2 = (m1+m1)/(m1+m2)v1 + (m2-m1)/(m1+m2)v2

And this all works well and good (I think)

However, I am having trouble doing the same thing for rotation: what's the equivalent formula for rotation? Are there rotational equivalents for mass, velocity, momentum, and kinetic energy, and how can I use a formula similar to the one above to, given rotational momentum, calculate rotational velocities after a collision?
 
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  • #2
p=I*w and KE=.5*I*w^2
where I is the moment of intertia and w is the angular frequency. p should be replaced with L to show that it is angular momentum.

L=m*(r cross v). the moment of inertia is the intergral of the distance (from the axis of rotation) squared over the entire mass
 
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  • #3
in a rotational system you have to replace conservation of momentum with conservation of angular momentum, but conservation of energy still works (you might have to add a potential term, depending on the situation).
Angular momentum L = mV x R (mass times velocity cross radius), if its circular motion then the cross product turns into simple multiplication L = mVR; keep in mind that the cross product gives you a ang mom vector perpendicular to the velocity and radius (use the right hand rule to get the sign correct + or -)
 
  • #4
i'm pretty sure its r cross v. point your hand away from the center and curl your fingers couterclockwise for an up moment and clockwise for a down moment.

nate, also notice that angular momentum can be written L=r cross p
 
  • #5
totally, sorry for the mistake. (also note that RxP = - PxR , which often leads to terms canceling in many-body systems)
 

1. What is conservation of kinetic energy in rotational motion?

In rotational motion, conservation of kinetic energy refers to the principle that the total kinetic energy of a rotating object remains constant as long as there is no external torque acting on it.

2. How is angular velocity related to kinetic energy in rotational motion?

The kinetic energy of a rotating object is directly proportional to the square of its angular velocity. This means that doubling the angular velocity will result in four times the kinetic energy.

3. Is conservation of kinetic energy applicable to all types of rotational motion?

Yes, conservation of kinetic energy applies to all types of rotational motion, including uniform circular motion, rolling motion, and rotational motion of rigid bodies.

4. What factors affect the conservation of kinetic energy in rotational motion?

The conservation of kinetic energy in rotational motion is affected by the moment of inertia, the angular velocity, and the mass distribution of the rotating object. Friction and air resistance can also affect the conservation of kinetic energy.

5. Can the total kinetic energy of a rotating object ever decrease?

No, according to the principle of conservation of energy, the total kinetic energy of a closed system cannot decrease. In rotational motion, this means that the total kinetic energy of a rotating object remains constant, unless there is an external torque acting on it.

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