A rope is wrapped around a wheel of radius R=2.0 meters. The wheel is mounted wi

Question

A rope is wrapped around a wheel of radius R=2.0 meters. The wheel is mounted with frictionless bearings on an axle through its center. A block of mass 14 kg is suspended from the end of the rope. When the system is released from rest it is observed that the block descends 10 meters in 2.0 seconds. What is the moment of inertia of the wheel? (hint-use energy conservation).

Please show all equations used, thank you!

Explanation / Answer

s= ut +0.5 at^2 => 10 = 0+ 0.5* a*2^2 =>a = 5 m/s^2 angular acceleration = a/r = 5/2 = 2.5 rad/s for the block; mg - T = ma => 14*9.8 -T = 14* 5 => T = 67.2 N for the pulley; torque = I* angular acceleration => T*r = I* 2.5 => 67.2*2 = I*2.5 => I = 53.76 kg-m2

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