Quick questions on Non-uniform circular motion (banked tracks, conical pendulums, vertical circles) explained: HSC Physics Module 5

On a frictionless banked track angled at $\theta$ to the horizontal, the normal force $N$ acts perpendicular to the road surface. Its horizontal component provides the centripetal force; its vertical component balances gravity.

For an object moving in a vertical circle (a ball on a string, a roller coaster loop), speed is not constant because gravity does work as the object rises and falls. At any point, the net force toward the centre still equals $\frac{m v^2}{r}$, but the contributions of tension and gravity vary around the loop.

Torque is the rotational equivalent of force, the tendency of a force to cause rotation about a pivot: