Question

Can the moment of force in a rotational motion be calculated by using both of these formulas: m.g.R(1-costheta) or m.g.R.theta

Answer 1

Yes, for very low angles:

$$1-\cos{\theta}=2\sin^2{(0.5\theta)}\\ \lim_{\theta\to0}{(1-\cos{\theta})}=0.5\theta$$