Question

Two drums are rolling down a hill. The drums are the same size and mass.

Drum #1 has most of its mass concentrated at the rim, while drum #2 has
most of its mass concentrated in the center. Which of the following
statements are correct? Select all that apply.
Drum #1 will reach the bottom of the hill first because its moment of inertia is
greater.
Drum #1 will have a greater center of mass speed and reach the bottom of the
hill first.
Drum #2 will have a greater center of mass speed and reach the bottom of the
hill first.
Drum #2 will reach the bottom of the hill first because its moment of inertia is
smaller.

Answer 1

Hi there!

Drum #2 will have a greater center of mass speed and reach the bottom of the hill first.

The moment of inertia can be thought of as inertia for rotation.

If mass is concentrated at the rim, the drum has a GREATER moment of inertia compared to if the mass is more concentrated towards the center.

Using the Rotational Equivalent of Newton's Second Law:

`\Sigma \tau = I\alpha`

**Sum of torques = Moment of inertia * angular acceleration

From this equation, we know that if 'I' increases, 'α' decreases, and thus, the speed of the object's center of mass decreases and it will reach the bottom later.

Therefore, drum #2 with the smaller moment of inertia (mass concentrated at the center) will have a greater angular acceleration ⇒ greater center of mass speed ⇒ read the bottom first.