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I was wondering if someone could help me out on this (taken from Newtonian Mechanics, A.P. French, pg 705, problem14-23)

A wheel of uniform thickness , of mass 10kg and radius 10cm is driven by a motor through a belt. The drive wheel on the motor is 2cm in radius. The motor is capable of delivering a torque of 5 Nm.

A) Assuming that the belt does not slip on the wheel, how long does it take to accelerate the large wheel from rest up to 100 rpm?

B) If the coefficient of friction between belt and wheel is 0.3, what are the tensions in the belt on the two sides of the wheel?

(Assume that the belt touches the wheel over half its circumference.)

For A, I had that if the belt does not slip, all of the torque is transferred to the driven wheel and I applied torque = moment X angular acceleration. And alpha = omega X time assuming alpha is constant.

For B, I thought of deriving friction from the normal force exerted by circumference on belt, but this looks like a nightmare to compute since the force the belt exerts on the circumference varies over the circumference.

In any case, does not the tension In a massless rope have to the the same on both sides always? If not we get infinite acceleration in any given differential element!

thanks.