Daily Practice Problems

📝 SolutionFor a uniform ring, mass is distributed symmetrically around the centre, so the centre of mass lies at the geometric centre, even though no material is actually there.

📝 SolutionTorque is the rotational analogue of force; it measures the tendency of a force to rotate a body about an axis, given by $\tau = rF\sin\theta$.

📝 SolutionTorque $\tau = \vec{r}\times\vec{F}$ has units of newton-metre (N·m); note it is dimensionally the same as energy but is a distinct vector quantity.

📝 SolutionMoment of inertia $I = \sum mr^2$ measures a body's resistance to change in rotational motion, just as mass measures resistance to change in linear motion.

📝 SolutionMoment of inertia depends both on the mass of the body and how that mass is distributed relative to the axis of rotation ($I = \sum mr^2$).