21 of 21 Incorrect Map d Sapling Learning macitan earning A student holds a bike

Question

21 of 21 Incorrect Map d Sapling Learning macitan earning A student holds a bike wheel and starts it spinning with an initial angular speed of 7.0 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 45.0 complete rotations. Assuming the frictional torque remains constant, how much more time will it take the bike wheel to come to a complete stop? Number -25 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 that was acting on the spinning wheel. Number N: m T0.135

Explanation / Answer

initial angular speed wo = 7 rotations per second

wo = 7*2pi rad/s = 44 rad/s

time interval t1 = 10 s

angular displacement theta = 45 rotations = 45*2pi radians

from equation of rotatory motion

theta = wo*t1 + (1/2)*alpha*t1^2

45*2*pi = 7*2pi*10 + (1/2)*alpha*10^2

alpha = -3.14 rad/s^2

(a)

as the wheel comes to rest

wf = 0

wf = wo + alpha*t2

0 = 7*2pi - pi*t2

t2 = 14 second

dt = t2 - t1

dt = 14 - 10 = 4 s

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(b)

moment of inertia I = m*r^2

torque = I*alpha = m*r^2*alpha

torque = 0.725*0.385^2*3.14 = 0.337 Nm

DONE please check the answer. any doubts post in comment box

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