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.

 

 

Given:

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

 

Find:

  1. aP
  2. ωA, αA
  3. ωB, αB

 

Video solution:

 

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

 

 

Interactive solution:

 

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.