A block of mass m = 1.4 kg is attached to a string that is wrapped around the circumference of a wheel of radius R = 7.0 cm. The wheel rotates freely about its axis and the string wraps around its circumference without slipping. Initially the wheel rotates with an angular speed omega, causing the block to rise with a linear speed v = 0.36 m/s.
Find the moment of inertia of the wheel if the block rises to a height of h = 6.8 cm before momentarily coming to rest.