3) A solid, uniform disk of mass 5 kg and radius 7 cm rotates without friction o

Question

3) A solid, uniform disk of mass 5 kg and radius 7 cm rotates without friction on an axle. Light string is wrapped around the periphery of the disk. The string is pulled so that its tension is a function of time given by T = 5(N/s2)t2. If the disk is initially at rest, what is its angular velocity at t = 9s?

Explanation / Answer

I = m*R^2/2 = 5*0.07^2/2 = 0.01225 kg-m^2 torque, T = T*R = (5*t^2)*0.07 = 0.35 *t^2 => I*alpha = 0.35*t^2 => 0.01225 *(dw/dt) = 0.35*t^2 => dw = [ 28.57 *t^2 ] dt Integrating both sides, we get; w = 28.57*(t^3/3) + c at t=0, w = 0 => 0 = 0 + c => c = 0 so, w = 28.57* (t^3/3) => w = 9.523 *t^3 => w (t = 9s) = 9.523 *9^3 = 6942.267 rad/s

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