Rotational Dynamics
Consider: S F = ma and t = r F sin(qrF) .
If we multiply both sides of S F = ma 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 .