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

A system consists of a disk rotating on a frictionless axle and a ball of clay moving toward it, as shown in the figure. At time $t=0$, the edge of the disk moves at a linear speed $v$, and the clay moves at speed $2v$. At time $t=t_0$, the clay sticks to the outside edge of the disk.

Which of the following graphs could represent the angular momentum of the system as a function of time?

A ball of mass $50\mathrm{g}$ is thrown at a door of mass $20\mathrm{kg}$. The ball strikes the center of the door perpendicularly with a velocity of $20\mathrm{m}/\mathrm{s}$ and rebounds at $15\mathrm{m}/\mathrm{s}$. The door has a height of $200\mathrm{cm}$ and a width of $80\mathrm{cm}$.

Taking the rotational inertia of the door about its hinges as $\frac{1}{3}M{L}^2$, which of the following is most nearly the angular speed of the door after the collision?

A tetherball is suspended from the top of a vertical stationary pole by a massless rope, as shown in the figure. The ball is given an initial speed $v$and the rope starts to wrap around the pole. The rotational inertia of the ball is $m{r}^2$, where $r$ is the distance between the ball and the pole.

Which of the following correctly represents the speed of the ball when the rope has become wrapped around the pole such that the distance between the ball and the pole has reduced by half?

A pottery wheel with a rotational inertia of $8.2\mathrm{kg}·{\mathrm{m}}^2$ rotates at a constant rate of $22\mathrm{rpm}$. The artist drops a lump of clay of mass $1.8\mathrm{kg}$ on the wheel, where it sticks at a distance of $46.0\mathrm{cm}$ from the axis of rotation.

If no net external torque acts on the system, which of the following is most nearly the angular speed of the wheel after the clay is dropped on it?

According to the accretion model of the Solar System, the planets formed from a slowly rotating nebula that collapsed under gravity.

Which of the following correctly describes why planets spin faster than the original nebula?

A circular track of mass $M$ is placed on a massless horizontal ring which is free to rotate about a frictionless vertical axis, as shown in the figure. A battery-driven toy car of mass $m$ is initially at rest on the track. As the car begins to move, it causes the track to rotate in the opposite direction. When the car moves with linear speed $v$, the angular speed of the ring is $\omega$. The distance from the axis to the ring's outer edge is $r$ and to the ring's inner edge is $\frac{3}{5}r$. The rotational inertia of the track-ring system is $I=\frac{1}{2}M\left(r_1^2+r_2^2\right)$, where $r_1$ is the inner radius and $r_2$ is the outer radius.

Which of the following expressions correctly represents the angular speed of the ring $\omega$?

An object of mass $m$ and speed $v$ collides and sticks to the rim of a wheel of radius $r$ and rotational inertia $\frac{1}{2}M{r}^2$ which is free to rotate about a frictionless axle at its center, as shown in the figure. Before the collision, the wheel is initially at rest.

Which of the following expressions correctly represents the linear speed of the object after the collision?

The main body of a satellite in space rotating with initial angular velocity ${\omega }_0$ can be modeled as a cylinder of rotational inertia $I_0$. When a system of solar panels unfolds and extends outward from the main body, the satellite then has rotational inertia $I_f$ and angular velocity ${\omega }_f$.

Which of the following is true about the rotational inertia and angular velocity of the satellite?

A uniform rod of mass $3\mathrm{kg}$ and length $L=1.2\mathrm{m}$ is free to rotate about a frictionless pivot at its upper end. Initially, the lower end of the rod hangs vertically at rest before being struck by an object of mass $1\mathrm{kg}$ traveling at a speed of $10\mathrm{m}/\mathrm{s}$ perpendicular to the rod. Immediately after the collision, the object moves at an angle $\theta$ below the horizontal, and the bar swings upward, coming to rest in a horizontal position, as shown in the figure. The rotational inertia of a rod about one of its ends is $\frac{1}{3}M{L}^2$.

If kinetic energy is conserved in the collision, which of the following is most nearly the magnitude and direction of the velocity of the object immediately after the collision?

Disk X rotates freely about a frictionless axle at its center. An identical disk Y, which is initially at rest, is dropped directly onto disk X and the two disks stick together, as shown in the figure.

How does the total angular momentum and total kinetic energy of the two-disk system compare to that of the system before disk Y was dropped?