15. Rotational Equilibrium

A composite disc is made out of two concentric cylinders, as shown. The inner cylinder has radius 30 cm. The outer cylinder has radius 50 cm. If you pull on a light rope attached to the edge of the outer cylinder (shown left) with 100 N, how hard must you pull on a light rope attached to the edge of the inner cylinder (shown right) so the disc does not spin?

A rectangular current loop of width $w$ and height $h$ carries a current $I$ and is placed in a uniform magnetic field $B$ such that the plane of the loop makes an angle $\theta$ with the magnetic field. What is the magnitude of the torque acting on the loop?

A pulley of radius $R$ has a rope wrapped around it with a tension $T$ acting tangentially. What is the net torque about the axle on the pulley?

In a system that is in rotational equilibrium, how do the clockwise and counterclockwise $\tau$ compare?