Rotational KE and L

A person sits on a freely spinning lab stool (no friction). When this person extends her arms,

• Her moment of inertia decreases and her angular velocity increases

• Her moment of inertia decreases and her angular velocity decreases

• Her moment of inertia increases and her angular velocity decreases

• Her moment of inertia increases and her angular velocity increases

A solid cylinder and a hollow cylinder have the same mass and the same radius. Which statement is true concerning their moment of inertia about an axis through the exact center of the flat surfaces?

• The hollow cylinder has the greater moment of inertia

• The solid cylinder has the greater moment of inertia

• Both cylinders have the same moment of inertia

• It depends how much material is removed from the hollow cylinder

In translational motion, mass is a measure of an object’s acceleration in response to a force. What is the rotational analog of mass?

• torque

• moment of inertia

• angular acceleration

• angular momentum

What is the angular momentum of the 2m-long, 2kg bar rotating about its center at 6 rad/s?

• 24 kgm²/s

• 2 kgm²/s

• 12 kgm²/s

• 4 kgm²/s

Three objects, A, B, and C all have the same mass and radius but different moments of Inertia. All three are released from the top of a ramp, which will reach the bottom of the ramp first?

• A

• B

• C

• They all tie

The turntable in a microwave oven has a moment of inertia of 0.040 kgm² and rotates continuously, making a complete revolution every 4.0 seconds. What is its kinetic energy?

• 0.099 J

• 0.314 J

• 0.05 J

• 0.0013 J

A ball with diameter 10. cm rolls without slipping on a horizontal table top. The moment of inertia of the ball is 2.2 × 10-3 kgm² and its translational speed is 0.45 m/s.

What is its angular speed about its center?

• 9 rad/s

• 0.09 rad/s

• 0.045 rad/s

• 4.5 rad/s

Two uniform disks have the same radius but different masses: disk 1 has a mass M, disk 2 has a mass 2M. What is the ratio of the moment of inertia of the first disk to the second disk?

• 1:4

• 1:2

• 2:1

• 4:1

Two uniform disks have the same radius but different radii: disk 1 has a radius R and disk 2 has a radius 2R. What is the ratio of the moment of inertia of the first disk to the second disk?

• 1:4

• 1:2

• 2:1

• 4:1

A ramp race between a Hoop, a Sphere, and an Ice cube takes place. All objects have the same mass, start from the same height at the same time. The Ice cube slides down the ramp with zero friction. Which object wins?

• Ice Cube

• Sphere

• Hoop

• They all tie