A uniform disk of mass 2.50 kg and radius 15.0 cm is free to rotate without fric

Question

A uniform disk of mass 2.50 kg and radius 15.0 cm is free to rotate without friction around a fixed horizontal axle passing through its center. A light thread is attached to the edge of the disk and wrapped around its circumference several times. The loose end of the thread is attached to a 0.50-kg mass that hangs freely from the thread. The disk and the hanging mass start from rest when the mass is released. Use the conservation of energy to determine the velocity of the mass after it has fallen 1.25 m.

Explanation / Answer

loss in PE = mgh = 0.5*9.8*1.25 = 6.125 J
gain in KE of mass = 0.5mv^2
gain in rotational KE of disc = 0.5*(0.5mr^2)(v/r)^2 = 0.25mv^2
so, from conservation of energy, 0.75mv^2 = 6.125 J
v = 1.80739 m/s

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