Pulley A Pulley A rotates clockwise at a constant angular velocity, driving a se

Question

Pulley A

Pulley A rotates clockwise at a constant angular velocity, driving a second larger Pulley B using a flexible belt moving around the two pulleys without slipping. The radius r_A for Pulley A is half of the radius r_n of Pulley B. (I) Is the magnitude of the angular velocity of Pulley A greater than, less than, or equal to the magnitude of the angular velocity of Pulley B? Explain. Is the magnitude of the linear velocity of a point on the edge of Pulley A greater than, less than, or equal to the magnitude of the linear velocity of a point on the edge of Pulley B? Explain. Is the direction of the angular velocity of Pulley A the same as, opposite to, or is it impossible to compare the direction of the angular velocity of Pulley B? Explain. Is the direction of the angular momentum of Pulley A the same as Pulley B, opposite to Pulley B, or is it impossible to compare the direction of the angular momenta of the two pulleys? Explain.

Explanation / Answer

1) Considering relation: A x rA = B x rB

Since rA = 0.5 x rB , therefore, B = 0.5 A

therefore A(angluar velocity of A) > B(angluar velocity of B)

2) Since, vA = A x rA = B x rB = vB

therefore velocity of A and B are same

3) Since A and B are in direct contact if A rotates clockwise then B should also rotate clockwise, therefore they are in same directions.

4) Angular momentum, L = I ,

Angular momentum will be in same direction as pulley B.

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