How do linear momentum and angular momentum compare?

Linear momentum: mass in motion in a straight line. Angular momentum: rotational inertia in motion around an axis.

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How do linear momentum and angular momentum compare?

Linear momentum: mass in motion in a straight line. Angular momentum: rotational inertia in motion around an axis.

What is the difference between torque and angular impulse?

Torque: A twisting force that causes rotation. Angular impulse: The change in angular momentum caused by a torque acting over a time interval.

Compare rigid and non-rigid systems in terms of angular momentum.

Rigid systems: Angular speed can only be changed by external torques. Non-rigid systems: Angular speed can be changed by altering mass distribution.

Compare the effects of internal and external torques on a system's angular momentum.

Internal Torques: Redistribute angular momentum within the system, but the total remains constant. External Torques: Change the total angular momentum of the system.

Compare linear impulse and angular impulse.

Linear Impulse: Change in linear momentum. Angular Impulse: Change in angular momentum.

How do you calculate angular impulse using torque?

Angular impulse can be calculated using the integral $\int \vec{\tau} dt$ or $\vec{\tau} \Delta t$ for a constant torque.

What is the process for determining total angular momentum of a system?

Calculate the angular momentum of each individual component relative to the axis of rotation, then add them together using superposition.

Describe the steps to analyze a collision involving rotating objects using angular momentum.

Identify if external torques are present. 2. If not, apply conservation of angular momentum: $L_{initial} = L_{final}$ . 3. Calculate initial and final angular momenta. 4. Solve for unknowns.

What is the process to determine the final angular velocity after a change in the moment of inertia?

Recognize that angular momentum is conserved ( $L = I\omega$ ). 2. Use $I_1\omega_1 = I_2\omega_2$ . 3. Solve for the final angular velocity $\omega_2$ .

How do you apply the angular impulse-momentum theorem?

Calculate the angular impulse: $\vec{\tau} \Delta t$ . 2. Set it equal to the change in angular momentum: $\Delta \vec{L} = \vec{\tau} \Delta t$ . 3. Solve for the desired quantity.

How do you calculate angular impulse?

Angular impulse can be calculated using the integral $\int \vec{\tau} dt$ or $\vec{\tau} \Delta t$ for a constant torque.

How do you find the total angular momentum of a system?

Add up the angular momenta of all its parts, considering each component's angular momentum relative to the axis of rotation.

What is the impulse-momentum theorem for rotational motion?

The change in angular momentum $\Delta \vec{L}$ is equal to the angular impulse.

How to determine the new angular speed when the moment of inertia changes in a closed system?

Since $L = I\omega$ is constant, if I decreases, then ω must increase proportionally to keep L constant.

How do you analyze collisions involving rotating objects using angular impulse?

Apply the principle of conservation of angular momentum, considering the angular impulse during the collision to relate initial and final angular momenta.

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How do linear momentum and angular momentum compare?

Linear momentum: mass in motion in a straight line. Angular momentum: rotational inertia in motion around an axis.

What is the difference between torque and angular impulse?

Torque: A twisting force that causes rotation. Angular impulse: The change in angular momentum caused by a torque acting over a time interval.

Compare rigid and non-rigid systems in terms of angular momentum.

Rigid systems: Angular speed can only be changed by external torques. Non-rigid systems: Angular speed can be changed by altering mass distribution.

Compare the effects of internal and external torques on a system's angular momentum.

Internal Torques: Redistribute angular momentum within the system, but the total remains constant. External Torques: Change the total angular momentum of the system.

Compare linear impulse and angular impulse.

Linear Impulse: Change in linear momentum. Angular Impulse: Change in angular momentum.

How do you calculate angular impulse using torque?

Angular impulse can be calculated using the integral $\int \vec{\tau} dt$ or $\vec{\tau} \Delta t$ for a constant torque.

What is the process for determining total angular momentum of a system?

Calculate the angular momentum of each individual component relative to the axis of rotation, then add them together using superposition.

Describe the steps to analyze a collision involving rotating objects using angular momentum.

Identify if external torques are present. 2. If not, apply conservation of angular momentum: $L_{initial} = L_{final}$ . 3. Calculate initial and final angular momenta. 4. Solve for unknowns.

What is the process to determine the final angular velocity after a change in the moment of inertia?

Recognize that angular momentum is conserved ( $L = I\omega$ ). 2. Use $I_1\omega_1 = I_2\omega_2$ . 3. Solve for the final angular velocity $\omega_2$ .

How do you apply the angular impulse-momentum theorem?

Calculate the angular impulse: $\vec{\tau} \Delta t$ . 2. Set it equal to the change in angular momentum: $\Delta \vec{L} = \vec{\tau} \Delta t$ . 3. Solve for the desired quantity.

How do you calculate angular impulse?

Angular impulse can be calculated using the integral $\int \vec{\tau} dt$ or $\vec{\tau} \Delta t$ for a constant torque.

How do you find the total angular momentum of a system?

Add up the angular momenta of all its parts, considering each component's angular momentum relative to the axis of rotation.

What is the impulse-momentum theorem for rotational motion?

The change in angular momentum $\Delta \vec{L}$ is equal to the angular impulse.

How to determine the new angular speed when the moment of inertia changes in a closed system?

Since $L = I\omega$ is constant, if I decreases, then ω must increase proportionally to keep L constant.

How do you analyze collisions involving rotating objects using angular impulse?

Apply the principle of conservation of angular momentum, considering the angular impulse during the collision to relate initial and final angular momenta.