Question

Rolling and slipping: A relative motion approach Mech Name HW-45 6. A cylinder of radius R is placed on top of a wooden board. They are initially at rest. The board is then pulled to the right by a constant horizontal force of magnitude F on a frictionless surface, The cvlinder is observed to roll counterclockwise without slipping cylinder wooden board on the board frictioniess surface At the instant that the board has speed vh, the center-of- mass of the cylinder has speed ., and the cylinder is rotating with angular velocity e For the tollowing questions, consider the time interval when the cylinder is still moving on the board. The cylinder is observed to roll counterclockwise without slipping on the board. Based on this observation, what do you know about the direction of horizontal force(s) that are acting on the cylinder? Explain. a. b. Based on your answer in part a, what is the direction of acceleration of the center-of-mass of the cylinder in the ground frame? Explain. What is the direction of the velocity of the center-of-mass of the cylinder in the ground frame? Explain. c. Consider the point on the cylinder that is in contact with the wooden board at some instant t. d. At that instant, in the ground frame, what is the magnitude of the velocity of that point in terms of v. R. and eo? Explain. Write an cquation that relates the quantities t. . R. and o. Explain. e.

Answer 1

a) It's clear that there is only 1 force acting horizontal on the cylinder and that is the friction between the plank and cylinder.

If the cylinder is rotating CCW than the friction is responsible for the rotation. It must act so that the torque about center rotates it CCW. So it must be acting in right direction.

b) As there is only one force on the cylinder in ground frame of reference so the acceleration must be in direction of that force. So the acceleration will be in direction of the frictional force which is acting towards right.

c) Initially it was at rest so the velocity will also be in direction of the acceleration. So it is right.

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