Properties of rotation dynamics?
- oldprofLv 79 years agoFavorite Answer
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.