Two spheres of equal size and equal mass are rotated with an...

Two spheres of equal size and equal mass are rotated with an equal amount of torque. One of the spheres is solid with its mass evenly distributed throughout its volume, and the other is hollow with all of its mass concentrated at the edges. Which sphere would rotate faster? (A) Solid sphere (B) Hollow sphere (C) They would rotate at equal rates. (D) Additional information is required to determine the relative rates of rotation.

Two spheres of equal size and equal mass are rotated with an equal
amount of torque. One of the spheres is solid with its mass evenly
distributed throughout its volume, and the other is hollow with all of
its mass concentrated at the edges. Which sphere would rotate faster?
(A) Solid sphere
(B) Hollow sphere
(C) They would rotate at equal rates.
(D) Additional information is required to determine the relative rates of rotation.

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Key Concepts

Mass Distribution

Mass distribution refers to how the mass of an object is arranged relative to the axis of rotation. A uniform, centrally concentrated mass distribution results in a lower moment of inertia compared to a mass distribution that is spread out or concentrated further from the center, affecting how quickly an object can accelerate rotationally.

Angular Acceleration

Angular acceleration is the rate at which an object's rotational velocity changes with time. It is directly proportional to the applied torque and inversely proportional to the moment of inertia, as stated by the equation: angular acceleration equals torque divided by moment of inertia.

Torque

Torque is the rotational equivalent of force; it causes objects to rotate about an axis. In rotational dynamics, the application of a torque is what produces angular acceleration in an object.

Moment of Inertia

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on both the total mass and how that mass is distributed with respect to the axis of rotation, with mass located further from the axis producing a higher moment of inertia.

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