Final answer:
The moment of inertia for a single point mass is given by I = mr² and for a hollow ring, it is I = MR². The distance from the axis of rotation to the mass is crucial, as a greater distance increases the moment of inertia.
Step-by-step explanation:
The moment of inertia (I) is a property of a physical body that determines how much torque it takes to change its angular velocity. For a single point mass, the moment of inertia is simply calculated as I = mr², where 'm' is the mass of the point and 'r' is the perpendicular distance from the rotation axis to the mass.
However, if we consider a hollow ring or hoop, which essentially is a collection of point masses all at the same distance 'R' from its center, the moment of inertia becomes I = MR², where 'M' is the total mass of the ring. This uniform distribution of mass at a constant radius means that all of the mass contributes to the moment of inertia equally.
It's important to note the dependency of the moment of inertia on the distribution of mass in relation to the axis of rotation. The farther the mass is distributed from the axis of rotation, the larger the moment of inertia. This can be seen in the comparison between a hollow ring and a solid disk of the same mass, where the hollow ring has a larger moment of inertia due to its mass being located further from the center.