Angular Momentum and Energy

A person sits on a freely spinning lab stool that has no friction in its axle. When this person extends her arms,

• her moment of inertia increases and her angular speed decreases.
• her moment of inertia decreases and her angular speed increases.
• her moment of inertia increases and her angular speed increases.
• her moment of inertia increases and her angular speed remains the same.

A uniform solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 33.4 rpm. What is its kinetic energy? (Hint: I=1/2 MR²⁾

• 0.092 J

• 17 J

• 1.1 J

• 0.18 J

A disk of mass m is spinning freely at 6.00 rad/s when a second identical disk, initially not spinning, is dropped onto it so that their axes coincide. In a short time the two disks are corotating. What is the angular speed of the new system?

• 3.00 rad/s

• 2.00 rad/s

• 12.0 rad/s

• 18.0 rad/s

Tags

NGSS.HS-PS2-2

If a wheel of moment of inertia 24 kg•m² moves at a velocity of 6 m/s and has an angular momentum of 36 kg•m²/s, what is its radius?

• 2 m
• 3 m
• 4 m
• 6 m

A system consists of a disk rotating on a frictionless axle and a piece of clay moving toward it, as shown in the figure above. The outside edge of the disk is moving at a linear speed v, and the clay is moving at speed v/2. The clay sticks to the outside edge of the disk. How does the angular momentum of the system after the clay sticks compare to the angular momentum of the system before the clay sticks, and what is an explanation for the comparison?

• It is the same because there is no external torque acting on the system

• It is greater because the rotating mass increases, which increases the rotational inertia.

• It is less because the speed of the disk decreases when the clay sticks to it.

• It is less because the angular momentum if the clay opposes that of the disk.

Tags

NGSS.HS-PS2-2

A disk of known radius and rotational inertia can rotate without friction in a horizontal plane around its fixed central axis. The disk has a cord of negligible mass wrapped around its edge. The disk is initially at rest, and the cord can be pulled to make the disk rotate. Which of the following procedures would best determine the relationship between applied torque and the resulting change in angular momentum of the disk?

• Pulling on the cord, exerting a force of 15 N for 2 s and then 25 N for 3 s, and measuring the final angular velocity of the disk

• For five forces of different time intervals, pulling on the cord for 5 s, exerting a force of 15 N, and then measuring the angle through which the disk rotates in each case

• For five forces of different time intervals, pulling on the cord for 5 s, exerting a force of 15 N, and then measuring the final angular velocity of the disk

• For five forces of different magnitude, pulling on the cord for 5 s, and then measuring the final angular velocity of the disk

Tags

NGSS.HS-PS2-1

A long rod is suspended by a frictionless bearing near its top. A lump of clay is projected from the right, collides with the block and sticks to it. Which one of the following statements is correct about the clay and rod system for this collision?

• The mechanical energy, linear momentum and angular momentum remain constant.

• The linear momentum and the angular momentum remain constant but the mechanical energy changes.

• Only the angular momentum remains constant.

• None of the quantities of mechanical energy, linear momentum, or angular momentum remain constant.

Tags

NGSS.HS-PS2-2

Which equation below illustrates conservation of angular momentum the best?

• $\Sigma p_0=\Sigma p_{f\ }$

• $\Sigma L_0=\Sigma L_f\$

• $\Sigma\tau_0=\Sigma\tau_f\$

• $\Sigma\omega_0=\Sigma\omega_{f\ }$

A given force is applied to a wrench to turn a bolt of specific rotational inertia I which rotates freely about its center.

Which of the following has the greatest angular acceleration?

• F

• A

• B

• E

• C

Tags

NGSS.HS-PS2-1