Introduction to SAT II Physics

The masses in the figure above are initially held at rest and are then released. If the mass of the

pulley is M, what is the angular acceleration of the pulley? The moment of inertia of a disk spinning

around its center is MR^2.

This is the only situation on SAT II Physics where you may encounter a pulley that is not
considered massless. Usually you can ignore the mass of the pulley block, but it matters when
your knowledge of rotational motion is being tested.
In order to solve this problem, we first need to determine the net torque acting on the pulley, and
then use Newton’s Second Law to determine the pulley’s angular acceleration. The weight of each
mass is transferred to the tension in the rope, and the two forces of tension on the pulley block
exert torques in opposite directions as illustrated below:

To calculate the torque one must take into account the tension in the ropes, the inertial resistance
to motion of the hanging masses, and the inertial resistence of the pulley itself. The sum of the
torques is given by:

Solve for the tensions using Newton’s second law. For Mass 1:

For Mass 2:

Remember that. Substitute into the first equation:

Because is positive, we know that the pulley will spin in the counterclockwise direction and the
3 m block will drop.

Kinetic Energy

There is a certain amount of energy associated with the rotational motion of a body, so that a ball
rolling down a hill does not accelerate in quite the same way as a block sliding down a frictionless