The disk has an initial clockwise rotation speed of 8 rad/sec and at t=0 begins

Question

The disk has an initial clockwise rotation speed of 8 rad/sec and at t=0 begins a counter-clockwise acceleration of ? = 0.6 t1.88. What is the speed of point A at t=3 sec? Point A has a radius of 2 ft.

Explanation / Answer

Call counterclockwise direction as positive. =>wo = -8 rad/sec alpha = 0.6*(t^1.88) dw/dt = 0.6*(t^1.88) =>dw = 0.6*(t^1.88)dt =>w = 0.6*(t^2.88)*(1/2.88) + C, where C is integration constant. But at t = 0, w = wo = -8 rad/sec =>C = -8 rad/sec =>w = -8 + 0.6t^(2.88)*(1/2.88) At t=3sec, w = -8+(0.6*(3^2.88)*(1/2.88)) = -3.069760961 rad/sec That is 3.069760961 rad/sec, clockwise Speed = v = rw = 3.069760961*2 = 6.139521922 ft/s

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