A 68-cm-diameter wheel accelerates uniformly about its center from 100 rpm to 25

Question

A 68-cm-diameter wheel accelerates uniformly about its center from 100 rpm to 250 rpm in 5.0 s .

A) Determine its angular acceleration.

B)   Determine the radial component of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. Don't forget that the wheel has an initial angular velocity when it started accelerating.

C) Determine the tangential component of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating.

Explanation / Answer

initial velocity w1 = 100 rpm = 100*2*pi/60 rad/s = 10.5 rad/s

final angular velocity w2 = 250 rpm = 21 rad/s

A)

angualr acceleration alpha = (w2-w1)/t = (21-10.5)/5 = 2.1 rad/s^2

B)

velocity after 2s w = w1 + alpha*t = 10.5 + (2.1*2) = 14.7 rad/s

ar = r*w^2 = 0.34*14.7^2 = 73.5 m/s^2

(C0

atan = r*alpha = 0.34*2.1 = 0.714 m/s^2

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