# Is Angular Velocity, Momentum, and Energy Frame Invariant

1. Oct 17, 2009

### e2m2a

In physics the translational kinetic energy of an object is frame dependent. That is, in the center of mass frame of the object, the kinetic energy is zero. In any other frame it is not. In fact, work itself is frame dependent. A force applied through a distance will give a change in kinetic energy of the object with respect to one frame, but in another frame the same force could go through a different displacement, hence, with respect to the other frame, a different work or change in kinetic energy will be observed. However, impulse seems to be frame invariant (if we are dealing with non-relativistive speeds). That is, a force applied to an object for a given time increment will cause a change in momentum of the object in one frame and will give that SAME change in momentum with respect to any other frame. (Remember, I am assuming sub-relativistic speeds.)
However, I don't see how this could apply to angular motion. If an observer in one frame applies a torque through an angular displacement on an object that is pivoted at one end, not through its center of mass, there will be an increase in the rotational kinetic energy equal to:

∆KE = 1/2 I ω²

Will the same change in rotational kinetic energy be observed in any other frame? That is, is angular work frame invariant at sub-relativistic speeds?