Torque & Acceleration (Rotational Dynamics) 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.Express your 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

Relationship between angular acceleration, α, and linear acceleration, a:

a=r·α

Torque:

τ=r·F

Torque and angular acceleration:

τ=I·α

Moment of inertia of a cylinder:

I=12mr2

where I is the moment of inertia.

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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.

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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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