For the following question rank the objects in order from greatest to least.
4. Which object would be the most difficult to begin spinning about its center of mass?
a.) Solid sphere
b.) Hollow sphere
c.) Hallow cylinder
d.) Solid disk
e.) Solid cylinder
To rank the objects in order from greatest to least difficulty to begin spinning about their center of mass, we need to consider their moments of inertia. The moment of inertia is a measure of an object's resistance to changes in its rotational motion.
The moment of inertia depends on the object's mass distribution and shape. Objects with mass distributed farther from their center of mass have a higher moment of inertia and are more difficult to spin.
Here are the objects listed in order from greatest to least difficulty to begin spinning about their center of mass:
1. Hollow cylinder (c): A hollow cylinder has a larger moment of inertia compared to the other objects listed. The mass is spread farther from the center, making it more difficult to rotate.
2. Solid disk (d): A solid disk has a smaller moment of inertia compared to a hollow cylinder but larger than the remaining objects. It is easier to start spinning compared to the hollow cylinder.
3. Solid cylinder (e): A solid cylinder has a smaller moment of inertia compared to both the hollow cylinder and the solid disk. It is easier to start spinning compared to the previous two objects.
4. Solid sphere (a): A solid sphere has a smaller moment of inertia compared to all of the objects listed. It is easier to start spinning compared to the previously mentioned objects.
5. Hollow sphere (b): A hollow sphere has the smallest moment of inertia among all the objects listed. It is the easiest to start spinning about its center of mass.
Therefore, the objects are ranked from the most difficult to the least difficult to begin spinning about their center of mass as follows: c, d, e, a, b.