Rotational Momentum

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.

A disk of known radius and rotational inertia can rotate with minimal friction in a horizontal plane around its fixed central axis. The disk is given an initial angular velocity, and then a second identical disk is dropped on top of the first. Which of the following procedures would best determine the relationship between initial and final angular momentum of the two disk system?

• Allowing the first disk to rotate for 3 s before dropping the second disk,then 5 s, then 10 s, and measuring the final angular velocity of the two disk system

• For angular speeds acting for five different time intervals, measure the angle through which the disk rotates before and after the drop

• Spin the first disk at five angular speeds of different magnitude, measure the angle through which the disk rotates before and after the drop

• Spin the first disk at five known angular speeds of different magnitude, then measure the final angular velocity of the two disk system right after the drop

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NGSS.HS-PS2-2

The wheel on a vehicle has a rotational inertia of 3.0 kg∙m². At the instant the wheel has a counterclockwise angular velocity of 5.0 rad/s, an average counterclockwise torque of 6.0 N∙m is applied, and continues for 2.0 seconds. What is the change in angular momentum of the wheel?

• 12 kg∙m²/s

• 15 kg∙m²/s

• 18 kg∙m²/s

• 30 kg∙m²/s

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NGSS.HS-PS2-2

Why are you more stable when riding a bicycle at a faster speed?

• You have more mass
• The wheels have angular momentum
• It's not easier to ride at a faster speed
• The bike has more momentum

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A spinning wheel will maintain its state of angular momentum unless acted on by an external torque.

• True
• False

According to the Law of Conservation of Angular Momentum, if I (momentum of inertia) increases, what will happen to ω?

• Decrease
• Stay the same
• Increase

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.

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NGSS.HS-PS2-2

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.

What happens to her angular velocity when a figure skater brings in her arms?

• Increases her angular velocity
• Decreases her angular velocity
• Has no affect

An object is spinning. Doubling the mass reduces the ω by half.

• True

• False