The experimental apparatus is shown below. A hanging mass is suspended by a string, which hangs over a pulley and is wrapped around the spindle on the main platter of the rotational motion apparatus. The hanging mass (m) will smoothly accelerate down under the influence of gravity. Let the total moment of inertia of (Spindle + Main platter) is Is. Radius of spindle is rs. And the radius pulley is rp and mass of pulley is Mp. And Let's approximate the pulley as a ring.
a) Draw the free-body diagram of the hanging mass, and write the equation of motion (equation about forces and acceleration)
b) The thread's tension T also applies a torque on the main platter via the spindle. Write the equation about the torque for the (spindle + platter) (for Newton's 2nd law for rotational motion with angular acceleration)
c) Write the equation about the torque for the pulley (for Newton's 2nd law for rotational motion with angular acceleration)