Question

After fixing a flat tire on a bicycle you give the wheel a spin. If its initial angular speed was 6.32 rad/s and it rotated 12.7 revolutions before coming to rest, what was its average angular acceleration (assuming that the angular acceleration is constant)?

For what length of time did the wheel rotate?

Answer 1

Solution)

Given,

Initial angular velocity, wo=6.32 rad/s

Final angular velocity, w'=0

Angular displacement, theta=12.7 revolutions=25.4 pi radians

Part a)

Average angular acceleration, alpha=(w^2- wo^2)/2theta

Substitute values,

Alpha=-(6.32)^2/ (2*25.4*pi)= -0.25 rad/s^2

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Time, t=(w-wo)/ alpha

Substitute values,

Time, t=- 6.32/(-0.25)= 25.23 s (Ans)

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