Angular Momentum & Angular Impulse (College Board AP® Physics 1: Algebra-Based): Exam Questions

Two identical rods, X and Y, each of length $L$ and mass $M$, are each made to rotate about different vertical axes, so they have different values of rotational inertia, as shown in the figure.

Which of the following expressions correctly relates the angular speeds of X and Y if they have equal angular momenta?

A rigid body consists of a vertical support post and two horizontal rods of negligible mass. Masses are attached to the ends of the horizontal rods, as shown in the figure. The body rotates about a vertical axis along the support post with constant angular speed $\omega$.

What is the ratio of the angular momentum of the two upper spheres to that of the two lower spheres?

A constant force of $250\mathrm{N}$ is applied tangentially to the outer edge of a playground merry-go-round of radius $2.0\mathrm{m}$ to rotate it from rest. A frictional force of $50\mathrm{N}$ is exerted tangentially at a distance of $25\mathrm{cm}$ from the axis of rotation. The rotational inertia of the merry-go-round is $1500\mathrm{kg}·{\mathrm{m}}^2$.

Which of the following is most nearly the angular speed of the merry-go-round if the force is applied for 5 seconds?

A disk with a rotational inertia of $0.11\mathrm{kg}·{\mathrm{m}}^2$ is mounted on a frictionless horizontal axle. The graph shows the torque applied to the outer rim of the disk as a function of time.

If the disk is initially at rest, what is the minimum time it takes for the disk to spin at a rate of 10 revolutions per second?

Two disks, X and Y, each experience a net external torque that varies over an interval of 10 seconds. Disk Y has a rotational inertia that is twice that of Disk X. The graph shown represents the angular momentum $L$ of the two disks as functions of time $t$ between $t=0$ and $t=10\mathrm{s}$. The average magnitudes of the net torques exerted on disks X and Y from $t=0$ to $t=10\mathrm{s}$ are ${\tau }_X$ and ${\tau }_Y$, respectively. At $t=10\mathrm{s}$, the angular speeds of disks X and Y are ${\omega }_X$ and ${\omega }_Y$, respectively.

Which of the following expressions correctly relates the magnitudes of the average torques and the magnitudes of the final angular speeds?

Two disks, A and B, rotate in opposite directions about fixed axles at their centers. The rotational inertia of Disk B is four times that of Disk A. Initially, Disk A has an angular velocity of $-{\omega }_0$ and Disk B has an angular velocity of $+{\omega }_0$. At time $t=0$ the disks experience net torques of varying magnitude. The graphs represent the net torques $\tau$ exerted on the two disks as functions of time $t$. From $t=0$ to $t=\frac{t_0}{2}$, the change in angular momenta of the disks are $∆L_A$ and $∆L_B$, respectively. At $t=\frac{t_0}{2}$, the angular speeds of disks A and B are ${\omega }_A$ and ${\omega }_B$, respectively.

If the final angular speed of Disk A is $3{\omega }_0$, which of the following is true about the change in angular momenta of the disks and their final angular velocities at $t=\frac{t_0}{2}$?

A uniform rod of mass $M=2\mathrm{kg}$ and length $L=1\mathrm{m}$ is free to rotate about a frictionless pivot which is positioned $\frac{L}{4}$ from its left end and held horizontally by a string of negligible mass at its right end, as shown in the figure. The rotational inertia of a rod about its center is $\frac{1}{12}M{L}^2$. The string is cut and releases the rod, allowing it to rotate about the pivot and swing down from the horizontal position.

Which of the following is most nearly the angular momentum of the rod when it reaches a vertical position?

A mass $M$ is attached to a light cord wrapped around a wheel which is mounted to a frictionless axle at its center, as shown in the figure. The wheel consists of two uniform rods, each of length $L$ and mass $M$, which are attached to a thin hoop of mass $M$. The rotational inertia of a rod about its center is $\frac{1}{12}M{L}^2$ and the rotational inertia of a thin hoop of radius $R$ is $M{R}^2$. The mass is released from rest.

Which of the following expressions represents the angular momentum of the mass-wheel system after the wheel has turned through one revolution?

A car wheel of rotational inertia $\frac{1}{2}m{r}^2=1.5\mathrm{kg}·{\mathrm{m}}^2$ is brought to rest by applying the brakes, which exert a frictional torque about the wheel's central axle. The graph shows the braking torque on the wheel as a function of angular position.

Assuming the wheel does not slip, which of the following is most nearly the change in angular momentum of the wheel?

A system consists of two objects, of masses $m$and $2m$, connected by a rod of length $L$ which has a negligible mass. The system is free to rotate about an axis twice as far away from mass $m$ as it is from mass $2m$, as shown in the figure. The system rotates with initial counterclockwise angular velocity ${\omega }_0$ and eventually comes to rest due to a frictional force between the objects and the surface, where the coefficient of friction is $\mu$.

Which of the following expressions represents the time taken for the system to come to rest?