A large spool of rope rolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance , holding onto it, Fig. 8-64. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool's center of mass move?
Step 1 of 2</p>
Let the radius of the spool be R, the linear speed of the CM be and the angular velocity of the spool be
Also, the speed of the person is the speed of the top most point of the spool and therefore