Question

Three objects, a solid sphere, a hollow ring, and a solid disk, have the same radius R. A string is wrapped around each object and the same tangential force is applied to each object at R and time t = 0 s. Which one of the following statements concerning the angular momentum of these objects after a short time t has elapsed, assuming the tangential force was continually applied? A. The angular momentum of the solid disk is larger than that of the other two objects. B. The angular momentum of the solid sphere is larger than that of the other two objects. C. The angular momentum of the hollow ring is larger than that of the other two objects D. The angular velocity of all of the objects has the same value. E. The angular velocity of the solid disk and hollow ring are equal, but that of the solid sphere is smaller.

Answer 1

The angular momentum of the solid sphere is larger than that of the other two objects.

Step-by-step explanation:

The angular momentum of an object depends on its moment of inertia and its angular velocity. In this case, all three objects have the same radius, so the moment of inertia is determined by the shape and mass distribution of the objects.

The moment of inertia of a solid disk is given by 1/2 * m * R^2, the moment of inertia of a hollow ring is given by m * R^2, and the moment of inertia of a solid sphere is given by 2/5 * m * R^2. Since the solid sphere has the largest moment of inertia, it will have the largest angular momentum.

Therefore, the correct statement is B. The angular momentum of the solid sphere is larger than that of the other two objects.

Answer 2

The statement that is true concerning the angular momentum of these objects is B. The angular momentum of the solid sphere is larger than that of the other two objects.

What is true of the angular momentum ?

Since the radius R is the same for all objects, the moment of inertia is directly proportional to the mass. Therefore, the solid sphere has the highest moment of inertia among the three objects.

The object with the highest moment of inertia (solid sphere) will have the highest angular momentum. The object with the lowest moment of inertia (hollow ring) will have the lowest angular momentum.

The solid disk falls in between in terms of angular momentum.