A block of mass m is attached to a string that is wrapped around the circumferen

Question

A block of mass m is attached to a string that is wrapped around the circumference of a wheel of radius R and moment of inertia I. The wheel rotates freely about its axis and the string wraps around its circumference without slipping (see example image: http://www.webassign.net/walker/10-55.gif). Suppose the block has a mass of 2.1 kg and an initial upward speed of 0.39 m/s.

Find the moment of inertia of the wheel if its radius is 8.0 cm and the block rises to a height of 8.4 cm before momentarily coming to rest.

I have tried so many different ways to attemp this problem, but cannot seem to get the answer correct. Please show all work so that I can understand the process of acquiring the answer and am able to calculate similar problems in the future. Many thanks!

Explanation / Answer

Final KE = 0

Final P.E = mgh = 2.1*9.8*0.084 = 1.7287 J

the initial KE of the rotating wheel. = 1/2*I*omega^2

omega = v/r = .39 /.08 = 4.875

I = 2*Initial KE / (omega^2)

= 2*1.7287/(4.875)^2 = 0.14547kg*m^2

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