Rotational Inertia & Angular Momentum (AP1)

The figure represents a stick of uniform density that is attached to a pivot at the right end and the marks are at 0.5 m intervals.

If all 4 forces are exerted on the stick, then what will be the angular momentum of the stick after 2.0 s?

• zero

A motor rotates a rod, as shown in the illustration. Students can adjust the speed the motor causes the rod to rotate. What needs to be measured in order for a student to determine the rod’s change in angular momentum after 8 s? Justify your answer...

• The mass of the rod, because the mass is related to the net force that is exerted on the rod

• The length of the rod, because the length of the rod is related to the rotational inertia of the rod.

• The average net torque applied to the rod, because the average net torque is related to the change in angular velocity of the rod.

• The average net force applied to the rod, because the average net force is related to the impulse of the rod.

A rod rests on a flat surface and is allowed to rotate around its pivot point when a net torque is applied. Data is collected and the result is shown in the graph to the left which shows the angular acceleration a as a function of time . How can the student use the graph to determine the angular momentum of the rod at 5 s?

• Determine the average angular acceleration from 0 s to 5 s and multiply the result by the rotational inertia of the rod.

• Determine the area bound by the curve and the horizontal axis from 0 s to 5 s and multiply the result by the rotational inertia of the rod.

• Determine the average slope of the curve from 0 s to 5 s and multiply the result by the rotational inertia of the rod.

• Multiply the angular acceleration at 5 s by the rotational inertia of the rod.

A ball of mass M swings in a horizontal circle at the end of a string of radius R. A student gradually pulls the string inward so the radius decreases (as shown in the figure to the right). Which of the following predictions is correct about the angular momentum and rotational inertia of the ball during this situation?

• The angular momentum of the ball increases. The rotational inertia of the ball about the axis of revolution decreases.

• The angular momentum of the ball increases. The rotational inertia of the ball about the axis of revolution stays the same.

• The angular momentum of the ball remains constant. The rotational inertia of the ball about the axis of revolution decreases.

• The angular momentum of the ball remains constant. The rotational inertia of the ball about the axis of revolution stays the same.

An ice skater begins spinning with her arms outstretched (figure 1), then she begins to bring her arms in (figure 2), until finally she has her arms next to her body (figure 3). In which configuration below does the ice skater have the greatest angular momentum?

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• All Configurations have the same angular momentum

A horizontal disk of radius 0.2m and mass 0.3kg is mounted on a central vertical axle so that a student can study the relationship between net torque and change in angular momentum of the disk. In the experiment, the student uses a force probe to collect data pertaining to the net torque exerted on the edge of the disk as a function of time, as shown in the graph. The disk is initially at rest. At what instant in time does the disk have the greatest angular momentum?

• 0.00 sec

• 1.00 sec

• 1.75 sec

• 2.50 s