A student holds a bike wheel and starts it spinning with an initial angular spee

Question

A student holds a bike wheel and starts it spinning with an initial angular speed of 9.0 rotations per second. The wheel is subject to some friction, so it gradually slows down. In the 10-s period following the initial spin, the bike wheel undergoes 77.5 complete rotations. the frictional torque remains constant, how much more time Delta fs will it take the bike wheel to come to a complete stop? Delta fs= Number s The bike wheel has a mass of 0.725 kg and a radius of 0.315 m. If all the mass of the wheel is assumed to be located on the rim, find the magnitude of the frictional torque Tf that was acting on the spinning wheel.tau t= Number N middot m

Explanation / Answer

Part A)

We need to find alpha using

Theta = wot + .5(alpha)t2

Theta = 77.5 (2pi) = 486.95 rad

Initial angular velocity = 9 rev/s which converts to 56.55 rad/s

So...486.95 = 56.55(10) + .5(alpha)(102)

alpha = -1.57 rad/s2

Then wf = wo + (alpha)t

wf = (9)(2pi) + (-1.57)(10)

wf = 40.84 rad/s

Finally wf = wo + (alpha)t

0 = 40.84 + (-1.57)t

t = 26 sec

Part B)

Torque = Fr = I(alpha) where I = mr2

F(.315) = (.725)(.315)2(1.57)

F = .359 N

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