# Pulley

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Two blocks of mass m and 3m are slug over a pulley by a massless rope. The massess are initially at the same height. The pulley is a uniform solid disk of mass 12m and radius R. The total length of the rope including the part that is slung over the pullley is L The masses are released at time t = 0

Determine the time it takes for the pulley to complete one revolution

Determine the time that it takes for the smaller mass to crash into the pulley.

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##### Solution Summary

The solution determines the time it takes for the pulley to complete one revolution and the time that it takes for the smaller mass to crash into the pulley.

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Torque acting on the pulley= (3m-m) x g x R= 2 m g R ----(1)

Torque= I alpha

Where I = moment of inertia = ½ M R ^2

And alpha = angular acceleration

M= mass of the pulley = 12 m

Therefore I= ½ x (12 m ) R ^2= 6 m R^2

Torque= I alpha = 6 m R^2 x alpha ----------(2)

Equating 1 and ...

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