Pure Rotation - Example Problem 4.2-7

In the following figure, mass C is attached to a rope that is wrapped around the outer edge of drum B. As mass C falls, the rope around the drum unrolls without slipping, causing the drum to rotate. This, in turn, causes pulley A to rotate due to the belt connecting the drum's inner radius and the pulley. Consider that mass C is released from rest and reaches a velocity of 1 m/s after it has fallen 30 cm. If the mass accelerates at a constant rate, find for the instant shown

1. the magnitude of the acceleration of point P on the outer surface of the drum,
2. the angular velocity and angular acceleration of drum B, and
3. the angular velocity and angular acceleration of pulley A.

Given:

• a_C = constant
• r_A = 0.5 m
• r_B = 1 m
• r_P = 1.2 m
• v_C0 = 0
• s_C = 30 cm

Find:

1. a_P
2. ω_A, α_A
3. ω_B, α_B

Think about how we can use the velocity and acceleration of block C to find the acceleration of point P.

Use the information that we know about the velocity of block C to find its acceleration.