Use conservation of energy to determine the angular speed of

Use conservation of energy to determine the angular speed of the spool shown in Figure P8.36 after the 3.00 kg bucket has fallen 4.05 m, starting from rest. The light string attached to the bucket is wrapped around the spool and does not slip as it unwinds.
1 . rad/s

Solution

Mass of he disc M= 5 kg

Radius R = 0.6m

MI of the disc

   I = MR² /2 = 5*0.6²/2 = 0.9 kg-m²

Change in PE as the bucket falls = mgh = 3*9.8*4.05 = 119.07 J

This must be equal to Rotational KE of the disc

             = I² /2 , where is the angular speed

             = 119.07

Angular speed = sqrt(2*119.07/0.9) = 16.27 rads/s