A block of mass m=2.2kg is attached to a string that is wrapped around the circu

Question

A block of mass m=2.2kg is attached to a string that is wrapped around the circumference of a wheel of radius R=8.1cm. The wheel rotates freely about its axis and the string wraps around its circumference without slipping. Initially the wheel rotates with an angular speed w, causing the block to rise with a linear speed v= 0.34m/s

(*Answer using two significant figures*)

Part A) Find the moment of inertia of the wheel if the blockrises to a height of h=7.5 cm before momentarily coming to rest.
I=?? kg x m^2

Explanation / Answer

v = 0.34 m/s, R = 8.1 cm

v = r w, w = 0.34 / 0.081 = 4.198 rad/s

Initial energy = 1/2 mv2 + 1/2 Iw2 = (0.5 * 2.2 * 0.342) + (0.5 * I * 4.1982) = 0.127 + 8.81 I

final energy = m g h = 2.2 * 9.81 * 7.5 * 10-2 = 1.62

1.62 = 0.127 + 8.81 I

I = 0.169 kg.m2

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