Newton's second law:
Angular and linear accelerations are related by:
Moment of inertia for a cylinder:
Torque in terms of angular acceleration:
Substituting for the moment of inertia and the expression of torque:
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.
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Torque on Discs & Pulleys concept. You can view video lessons to learn Torque on Discs & Pulleys. Or if you need more Torque on Discs & Pulleys practice, you can also practice Torque on Discs & Pulleys practice problems.
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Based on our data, we think this problem is relevant for Professor Corrado's class at UCD.