Angular Acceleration of a Pulley

Learning Goal:

To understand rotation about a fixed axis using a kinetic approach.

As shown, a massless string is wrapped around a pulley of radius r and mass m. (Figure 1) The string’s other end is attached to a block with mass m. The pulley can rotate freely about its axis and its cylinder is uniform. Note that the positive y direction is downward and that counterclockwise moments are positive. 

 

 

 

Part A - Magnitude of the pulley’s angular acceleration

Find α, the magnitude of the pulley’s angular acceleration as the block descends.

Express your answer in terms of r and g, the magnitude of the acceleration due to gravity.

α =

g1.5r