Compare and contrast linear and angular momentum.

Linear momentum: mass in linear motion. Angular momentum: moment of inertia in rotational motion. Both are conserved in closed systems.

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Compare and contrast linear and angular momentum.

Linear momentum: mass in linear motion. Angular momentum: moment of inertia in rotational motion. Both are conserved in closed systems.

Compare the effect on final angular speed when a disk sticks versus bounces off a rod.

Sticking: Rod gains angular momentum. Bouncing: Disk transfers more angular momentum, so the rod's angular speed will be greater.

In the skater example, describe what happens to I and $\omega$ when the skater pulls their arms in.

Moment of inertia (I) decreases because mass is closer to the axis of rotation. Angular velocity ( $\omega$ ) increases to conserve angular momentum.

In the planetary motion diagram, explain why angular momentum is conserved.

Gravitational force is a central force, resulting in no external torque on the planet. Therefore, angular momentum is conserved.

What are the steps to solve a conservation of angular momentum problem?

1: Identify initial and final states. 2: Determine if external torque is zero. 3: Apply $L_{initial} = L_{final}$ . 4: Solve for the unknown.

How does a skater conserve angular momentum?

1: Skater starts spinning with arms out (high $I$ , low $\omega$ ). 2: Skater pulls arms in (low $I$ ). 3: Angular velocity increases to conserve angular momentum ( $L$ remains constant).