Question

Rank these by moments of inertias: a hollow cylinder, a hollow sphere, a solid cylinder, and a solid sphere. and explain why

Answer 1

When ranking objects by their moments of inertia from lowest to highest, the order would be as follows:

Hollow sphere: A hollow sphere has the lowest moment of inertia among the given objects. This is because the mass is distributed farther away from the axis of rotation, resulting in a larger radius of gyration and a lower resistance to changes in rotational motion.

Solid sphere: A solid sphere has a slightly higher moment of inertia compared to a hollow sphere. The mass is evenly distributed throughout the object, resulting in a smaller radius of gyration compared to the hollow sphere.

Hollow cylinder: A hollow cylinder has a higher moment of inertia compared to a solid sphere. The mass is distributed farther away from the axis of rotation, similar to the hollow sphere. However, the cylindrical shape with a larger radius of gyration contributes to a higher moment of inertia.

Solid cylinder: A solid cylinder has the highest moment of inertia among the given objects. The mass is distributed evenly throughout the object, but its cylindrical shape and smaller radius of gyration result in a higher resistance to changes in rotational motion compared to the other objects.

The moment of inertia depends on the distribution of mass around the axis of rotation. Objects with more mass concentrated farther away from the axis have higher moments of inertia, while objects with mass distributed closer to the axis have lower moments of inertia.

If you want to learn more about inertia and its principles, as well as many other interesting and fun science topics, read "Physics for entertainment" by Yakov Perelman. It is a great book with many practical scenarios.

~~~Harsha~~~

Answer 2

The ranking of moments of inertia is as follows: hollow cylinder > hollow sphere > solid cylinder > solid sphere.

Step-by-step explanation:

The moments of inertia can be ranked as follows:

1. Hollow cylinder: It has the largest moment of inertia for a given radius and mass.
2. Hollow sphere: It has a smaller moment of inertia compared to the hollow cylinder.
3. Solid cylinder: It has a larger moment of inertia compared to the hollow sphere.
4. Solid sphere: It has the smallest moment of inertia among the given objects.

The moments of inertia depend on the mass distribution and the axis of rotation. The hollow cylinder has more mass located far from its axis of rotation, resulting in a larger moment of inertia. Similarly, the hollow sphere and solid cylinder have different mass distributions contributing to their respective moments of inertia.