Rotational Dynamics
Consider: S F = ma . t = r F sin(qrF) .
If we multiply both sides by r sin(qrF) we get
S t = m a r sin(qrF) , but a sin(qra) = aq = ar, so S t = mr2a . If the mass is distributed at various radii, then the mr2 becomes S miri2 .
We define the moment of inertia be be
I = S miri2 so that we have S t = Ia .