please give step by step solution! thank you!! A student hold a bike wheel and s

Question

please give step by step solution! thank you!!

A student hold 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 fallowing the initial spin, the bike wheel undergoes 80.0 complete rotations. Assuming the frictional torque remains constant, how much more time Deltats will it take the bike wheel to come to a complete stop?. The bike wheel has a mass of 0.625kg and a radius of 0.385m. If all the mass of the wheel is assumed to be located on the rim, find the magnitude of the frictional torque tauf that was acting on the spinning wheel.

Explanation / Answer

initial speed , u = 9 rotation / sec
s = no. of rotation = 80
time (t) = 10 secs
Let the angular accelearion be a ..

so.. s = ut + 0.5 * a * t^2
so.. 80 = (9*10) + ( 0.5 * a * 10^2 )

so.. a = -0.2 rev / sec2

so.. total time needed to stop = u / a = 9 / 0.2 = 45 secs ...

so... delta ts = 45 - 10 = 35 secs


angular retardation = 0.2 rev / sec2 = 0.2 * 2pi = 1.256637 rad / sec^2
inertia of wheel = m*r^2 = 0.625*0.385^2 = 0.092640625 kg m^2

so torque = inertia * angular acceleraion = 1.256637 * 0.092640625 = 0.11641564 Nm

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