# Properties of rotation dynamics?

Rotation dynamics

Relevance

The cool thing about angular dynamics is that each property has its counterpart in linear dynamics. So if you know the liner stuff, like F = MA or KE = 1/2 MV^2, you can quickly write down the angular analogs. In fact, let's do that.

F = MA becomes torque = I alpha; where I = kMR^2 is the moment of inertia and alpha = A/R is the angular acceleration. k is a constant that depends on the shape and distribution of mass; you have to look it up most of the time.

Look at torque = I alpha = kMR^2 * A/R = kMA R = kF R. And there you are. Torque is the twisting force F = MA when applied to a radius of rotation R. In other words torque is just F = MA with a twist...ar, ar, ar.

and KE = 1/2 MV^2 becomes 1/2 IW^2; where I is the same I as before and W = V/R is the angular speed in radians/second. V is the tangential speed, which is a linear speed.

Now angular kinetic energy is KEa = 1/2 IW^2 = 1/2 kMR^2 W^2 = 1/2 kMV^2 = k KE And we see once again that the angular dynamics can be written in terms of the linear dynamics.

So, bottom line...substitute I for M and W for V and you'll have the angular dynamic analog to the linear property.