Question

A motor exerts torque on a carousel for it to attain a speed of 2.5 rev/s starting from rest in 3.5 s. Find the work done by the motor if the carousel has a radius of 27 m and mass of 1.75 x10^5kg. Consider

the carousel to be a thin-walled cylinder rotating about its center.

Answer 1

$\text{for thin-walled cylinder:}$

$I = mr^2$

$I = 1.75*10^5*27^2\approx1.28*10^8\ kg*m^2$

$W = I\phi,\text{where }\phi -\text{the rotation angle of the carousel in radians}$

$w_0 = 0$

$w_1= 2.5\frac{rev}{s}=5\pi\frac{rad}{s}$

$t = 3.5s$

$\epsilon= \frac{w_1-w_0}{t}=4.49\frac{rad}{s^2}$

$\phi = w_0t+\frac{\epsilon t^2}{2}= \frac{4.49*3.5^2}{2}=27.50\ rad$

$W = I\phi= 1.28*10^8*27.50 = 3.52*10^9 J$

$\text{Answer: }3.52*10^9 J$