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 it circumference several times. The loose end of the thread is attached to a 0.50-kg mass that hangs free 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 in m/s of the mass after it has fallen 1.25 m.

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Explanation / Answer

here,

mass of disk , m1 = 2.5 kg

radius , r1 = 0.15 m

mass attached , m2 = 0.5 kg

s = 1.25 m

let the velocity be v

using conservation iof energy

potential energy lost = kinetic energy gained

m2 * g * s = 0.5 * m2 * v^2 + 0.5 * I * w^2

m2 * g * s = 0.5 * m2 * v^2 + 0.5 * (0.5 * m1 * r^2) * (v/r)^2

2.5 * 9.81 * 1.25 = 0.5 * 0.5 * v^2 + 0.5 * 0.5 * 2.5 * v^2

solving for v

v = 5.92 m/s

the final speed is 5.92 m/s

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