Conceptual Dynamics - Independent Learning

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.




  • aC = constant
  • rA = 0.5 m
  • rB = 1 m
  • rP = 1.2 m
  • vC0 = 0
  • sC = 30 cm



  1. aP
  2. ωA, αA
  3. ωB, αB


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.