A vacuum cleaner belt is looped over a shaft of radius 0.48cm and a wheel of rad

Question

A vacuum cleaner belt is looped over a shaft of radius 0.48cm and a wheel of radius 2.20cm . The arrangement of the belt, shaft, and wheel is similar to that of the chain and sprockets in the figure. The motor turns the shaft at rotational velocity ? = 65.0rev/s and the moving belt turns the wheel, that in turn is connected by another shaft to the roller that beats the dirt out of the rug being vacuumed. Assume that the belt doesn't slip on either the shaft or the wheel.

What is the speed of a point on the belt? v=??m/s

What is the angular velocity of the wheel in rad/s?

Explanation / Answer

The belt will be moving at
w*r where w is the rotational velocity and r is the radius of the shaft

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