AP Physics C Mechanics Quiz: Angular Momentum And Angular Impulse

A spacecraft with $I=80\ \text{kg·m}^2$ must reach $\omega=0.60\ \text{rad/s}$ from rest; during a short burn, external torques are negligible except for the thrusters, so $J=\Delta L=I\Delta\omega$. Assume the torque direction matches the desired rotation. Considering the described system, calculate the angular impulse applied to the spacecraft during the interval.

An ice skater rotates about a vertical axis with $I_i=3.0\ \text{kg·m}^2$ and $\omega_i=2.0\ \text{rad/s}$. The skater pulls in arms to $I_f=1.2\ \text{kg·m}^2$ with negligible external torque, so $L=I\omega$ is conserved. Considering the described system, what is the final angular velocity of the system after the skater pulls in arms?

A wind turbine rotor with $I=2.0\times10^4\ \text{kg·m}^2$ spins at $\omega_i=0.80\ \text{rad/s}$. The wind drops and net torque becomes $\tau=-2.0\times10^3\ \text{N·m}$ for $t=4.0\ \text{s}$, using $\Delta L=\tau t$ and $L=I\omega$. Considering the described system, what is the final angular velocity of the system after 4.0 seconds?

A wind turbine rotor with $I=1.0\times10^3\ \text{kg·m}^2$ spins at $\omega_i=2.0\ \text{rad/s}$; the wind drops and the net torque becomes $\tau=-200\ \text{N·m}$ for $t=5.0\ \text{s}$, so $\Delta L=\tau t$ and $L=I\omega$. Neglect other torques. Based on the scenario above, what is the final angular velocity of the system after 5.0 seconds?

A solid disk with $I=0.80\ \text{kg·m}^2$ rotates at $\omega_i=12\ \text{rad/s}$. A motor applies constant torque $\tau=3.2\ \text{N·m}$ for $t=5.0\ \text{s}$, so $\Delta L=\tau t$. Based on the scenario above, what is the final angular velocity of the system after 5.0 seconds?

A rotating disk has $I=0.50\ \text{kg·m}^2$ and $\omega_i=16\ \text{rad/s}$. An external torque $\tau=1.5\ \text{N·m}$ acts for $t=4.0\ \text{s}$, so $\Delta L=\tau t$ and $L=I\omega$. Based on the scenario above, determine the change in angular momentum of the disk.

A spacecraft has rotational inertia $I=120\ \text{kg·m}^2$ about its yaw axis and initially $\omega_i=0$; its thrusters provide a constant torque $\tau=30\ \text{N·m}$ for $t=4.0\ \text{s}$, with angular impulse $J=\tau t=\Delta L$. Ignore external torques from space. Based on the scenario above, calculate the angular impulse applied to the spacecraft during the interval.

A bicycle wheel with moment of inertia $I=0.60\ \text{kg·m}^2$ starts from rest; a tangential force $F=18\ \text{N}$ is applied at the rim of radius $r=0.35\ \text{m}$ for $t=2.0\ \text{s}$, so $\tau=rF$ and $\Delta L=\tau t$. Neglect friction and assume the force stays perpendicular to the radius. Considering the described system, determine the change in angular momentum of the wheel.

A bicycle wheel with $I=0.40\ \text{kg·m}^2$ starts from rest; a constant tangential force $F=10\ \text{N}$ is applied at radius $r=0.30\ \text{m}$ for $t=5.0\ \text{s}$, so $\tau=rF$ and $\Delta L=\tau t$. Ignore friction and keep the force perpendicular to the radius. Based on the scenario above, determine the change in angular momentum of the wheel.

An ice skater spins with $I_i=3.0\ \text{kg·m}^2$ at $\omega_i=2.5\ \text{rad/s}$; they pull in their arms to $I_f=1.2\ \text{kg·m}^2$ while external torque is negligible, so $L=I\omega$ is conserved. Assume the change happens quickly compared with frictional effects. Considering the described system, what is the final angular velocity after pulling in their arms?

A wind turbine rotor has $I=1.0\times10^4\ \text{kg·m}^2$ and spins at $\omega_0=2.0\ \text{rad/s}$. The wind suddenly drops so external torque is approximately zero for $t=20\ \text{s}$, with $\tau=\Delta L/\Delta t$ and $L=I\omega$. Considering the described system, what is the effect of removing an external force on the system's rotation?

A wind turbine rotor has $I=5.0\times10^3\ \text{kg·m}^2$ and spins at $\omega_i=1.5\ \text{rad/s}$. A gust produces constant net torque $\tau=1.0\times10^3\ \text{N·m}$ for $t=6.0\ \text{s}$, with $\Delta L=\tau t$. Considering the described system, determine the change in angular momentum of the turbine.

A spacecraft has moment of inertia $I=1200\ \text{kg·m}^2$ about its yaw axis and initially $\omega_i=0$. Its attitude-control thrusters provide a constant torque $\tau=240\ \text{N·m}$ for $t=3.0\ \text{s}$, so angular impulse $J=\tau t=\Delta L$. Based on the scenario above, calculate the angular impulse applied to the spacecraft during the interval.

A uniform disk of radius $R$ and mass $M$ rotates about its center with angular velocity $\omega_0$. A second identical disk, initially not rotating, is dropped onto the first disk so that their axes coincide. Due to friction between the surfaces, they eventually rotate together. During this process, the angular impulse experienced by the initially stationary disk is:

A uniform sphere of radius $R$ and mass $M$ rolls without slipping down an inclined plane. When the sphere has descended a vertical distance $h$, its angular momentum about its center of mass is $L_{cm}$. What is the angular momentum of the sphere about a point on the inclined surface directly below the sphere's center?

A uniform thin hoop of mass $M$ and radius $R$ rotates freely about a vertical axis through its center with angular velocity $\omega$. A small mass $m$ (where $m \ll M$) slides radially outward along a spoke from the center to the rim. During this process, which statement about the angular impulse on the small mass is correct?

Two identical uniform rods, each of mass $M$ and length $L$, are initially at rest. Rod A lies along the x-axis with its center at the origin. Rod B lies along the y-axis with its center also at the origin, forming a cross. A brief torque is applied about the z-axis (perpendicular to both rods) to the entire system, giving it an angular impulse $J$. What is the final angular momentum of rod A about the origin?

A rigid body rotates about a fixed axis with moment of inertia $I$. A constant torque $\tau$ acts on the body for time $t$, changing its angular velocity from $\omega_1$ to $\omega_2$. If the same angular impulse were applied over a time interval $2t$ (with appropriately reduced torque), and the body started from rest, what would be its final angular velocity?

A particle of mass $m$ is attached to a string of length $\ell$ and swings as a pendulum. At the bottom of its swing, the particle has speed $v$. At this instant, a horizontal impulse $J$ is applied to the particle in the direction perpendicular to its velocity. What is the change in angular momentum about the pivot point?

A figure skater performs a spin with arms extended, having moment of inertia $I_1$ and angular velocity $\omega_1$. She then pulls her arms inward, reducing her moment of inertia to $I_2 = \frac{I_1}{3}$. If this process takes time $\Delta t$, what is the average torque that her muscles exerted during the arm-pulling motion?