Torque on Discs & Pulleys Video Lessons

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Problem: A string is wrapped around a uniform solid cylinder of radius r, as shown in the figure (Figure 1). The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m. Note that the positive y direction is downward and counterclockwise torques are positive. Find the magnitude α of the angular acceleration of the cylinder as the block descends. Expressyour answer in terms of the cylinder's radius r and the magnitude of the acceleration due to gravity g.

FREE Expert Solution

Newton's second law:

ΣF=ma

Angular and linear accelerations are related by:

a=rα

Torque:

τ=rT

Moment of inertia for a cylinder:

I=12mr2

Torque in terms of angular acceleration:

τ=Iα

Substituting for the moment of inertia and the expression of torque:

rT=(12mr2)αT=12mrα

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Problem Details

A string is wrapped around a uniform solid cylinder of radius r, as shown in the figure (Figure 1). The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m. Note that the positive y direction is downward and counterclockwise torques are positive. 

Find the magnitude α of the angular acceleration of the cylinder as the block descends. Express
your answer in terms of the cylinder's radius r and the magnitude of the acceleration due to gravity g.

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