Physics 207 WebPages - Fall 1999

Problem 9 (Problem 73 in Textbook)

Two uniform solid spheres have the same mass, 1.65 kg, but one has a radius of 0.226 m while the other has a radius of 0.854 m.

(a) For each of the spheres, find the torque required to bring the sphere from rest to an angular velocity of 317 rad/s in 15.5 s. Each sphere rotates about an axis through its center.

Solution:

We first find the rotational inertia from an equation in Table 11-2. Then we find the constant angular acceleration from the given information.

Setting up the equation, we obtain the following for the small sphere.

Also setting up the equation, we obtain the following for the large sphere.

(b) For each sphere, what force applied tangentially at the equator would provide the needed torque?

Solution:

Using the previous result for the small sphere, we obtain the following setup.

Also using the previous result for the large sphere, we obtain the following setup.

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