PLEASE DO NOT ROUND .. KEEP AT 3 SIG FIGS Question 12 of 16 sapling learning A s

Question

PLEASE DO NOT ROUND .. KEEP AT 3 SIG FIGS

Question 12 of 16 sapling learning 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 will it take the bike wheel to come to a complete stop? Number The bike wheel has a mass of 0.825 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

Explanation / Answer

Here

initial angular speed , wi = 9 rev/s

wi = 9 * 2pi rad/s

wi = 56.6 rad/s

in 10 s

angle = 77.5 rev = 486.9 rad

let the angular acceleration is a

Using second equation of motion

theta = wi * t + 0.5 * a * t^2

486.9 = 56.6 * 10 + 0.5 * a * 10^2

solving for a

a = -1.582 rad/s^2

let the total time taken to stop is t

Using first equation of motion

0 = 56.6 - 1.582 * t

t = 35.8 s

additional time taken to stop = 35.8 - 10

additional time taken to stop = 25.8 s

b)

magnitude of frictional torque = I * a

magnitude of frictional torque = m * r^2 * a

magnitude of frictional torque = 0.825 * 0.385^2 * 1.582

magnitude of frictional torque = 0.193 N.m

the magnitude of frictional torque acting on the wheel is 0.193 N.m

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