of 25 Map pling Learning lan learnig A student holds a bike wheel and starts it
ID: 2035310 • Letter: O
Question
of 25 Map pling Learning lan learnig 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 inital spin the bike wheel undergoes 77.5 complete rotations Assuming the frictional torque remains constant, how much more time At will it take the bike wheel to come to a complete stop? Number Ar, The bike wheel has a mass of 0.725 kg and a radius of 0.385 m. If all the mass of the wheel is assumed to be located on the rim, find the magnitude of the frictional torque ty that was acting on the spinning wheel. Number N·m Previous& Give Up & View Solution Check AnswerxtExit ntExplanation / Answer
given
angular speed of bike wheel, wi = 9 rps = 56.548667764616278 rad/s
in t = 10s, theta = 77.5 rotations
hence let angulat deceleration be alpha
then
theta = w1*t - 0.5*alpha*t^2
77.5 = 9*10 - 0.5*alpha*100
alpha = 0.25 rounds per second per second
hence additional time to come to stop = dt
then
wi = alpha*(t + dt)
dt = 26 seconds
m = 0.725 kg
r = 0.385 m
frictional torque = T
then
T = I*alpha
I = 0.5mr^2 = 0.5*0.725*0.385^2 = 0.0537315625 kg m^2
hence
T = 0.08440134100795041237726 Nm = 84.40134100795 m Nm
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