The pulley pictured has a rotational inertia of $$\frac{1}{2}MR^2$$   and has a weight of mass $$m_b$$   hanging to the right. The pulley starts from rest and the $$m_b$$   is allowed to fall for a time interval of time t (before hitting the ground). What is the angular momentum of the pulley after the time interval?

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...

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?

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?

A student spins around in a chair with arms outstretched holding weights. The initial angular velocity of the student is 1.2 $$\frac{rad}{s}$$   and their rotational inertia is 6 $$kg\cdot m^2$$  . The student then pulls the weights close to their body changing their rotational inertia to 2 $$kg\cdot m^2$$  . What is the new angular velocity w of the student?

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?

A disk rotates ith an angular speed of 30 rad/s. An identical disk is held at rest above the rotating disk and is then gently dropped on the rotating disk, as shown in figure 1. The two-disk system then rotates with a common angular speed $$\omega_1$$  . A third identical disk is held at rest above the two-disk system and again gently dropped on the rotating two-disk system, as shown in figure 2. The three-disk system then rotates with a common angular speed $$\omega_2$$  . What is the value of $$\omega_2$$  ?

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?

Two identical disks rotate about their centers in opposite directions with the same magnitude of angular speed $$\omega_0$$  . The top disk is dropped onto the bottom disk, as shown in the figure, so they collide and stick together. Which of the following predictions is correct about the motion of each individual disk after the collision?