Newton's second law:
Relationship between angular acceleration, α, and linear acceleration, a:
Torque and angular acceleration:
Moment of inertia of a cylinder:
where I is the moment of inertia.
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 & Acceleration (Rotational Dynamics) concept. You can view video lessons to learn Torque & Acceleration (Rotational Dynamics). Or if you need more Torque & Acceleration (Rotational Dynamics) practice, you can also practice Torque & Acceleration (Rotational Dynamics) practice problems.
What professor is this problem relevant for?
Based on our data, we think this problem is relevant for Professor Karkare's class at ASU.