A cable is wrapped several times around a uniform solid cylinder with diameter 0

Question

A cable is wrapped several times around a uniform solid cylinder with diameter 0.12 m and mass 50 kgthat can rotate freely about its axis. The cable is pulled by a force with magnitude 9.0 N. Assuming that the cable unwinds without stretching or slipping, find the magnitude of its acceleration.To wind the winch back up, you exert a force that points straight down on its rightmost edge. What is the magnitude of the force you need to exert if you wind the winch with an angular acceleration of 5.9 rad/s2?

Explanation / Answer

moment of inertia of cylinder = 0.5 * mass * radius^2

moment of inertia of cylinder = 0.5 * 50 * 0.06^2

torque = moment of inertia * angular acceleration

torque = force * radius

force * radius = moment of inertia * angular acceleration

9 * 0.06 = 0.5 * 50 * 0.06^2 * angular acceleration

angular acceleration = 6 rad/sec^2

force * 0.06 = 0.5 * 50 * 0.06^2 * 5.9

force = 8.85 N

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