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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.

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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.

What are the key differences between linear momentum and angular momentum?

Linear Momentum: Associated with translational motion, $\vec{p} = m\vec{v}$ . Angular Momentum: Associated with rotational motion, $\vec{L} = I\vec{\omega}$ or $\vec{L} = \vec{r} \times \vec{p}$ .

Compare and contrast linear impulse and angular impulse.

Linear Impulse: Change in linear momentum, $\vec{J} = \int \vec{F} dt = \Delta \vec{p}$ . Angular Impulse: Change in angular momentum, $\int \vec{\tau} dt = \Delta \vec{L}$ . Both are vector quantities.

Differentiate between torque and force.

Force: A push or pull that causes linear acceleration. Torque: A twisting force that causes angular acceleration.

Compare and contrast moment of inertia and mass.

Mass: Measure of an object's resistance to linear acceleration. Moment of Inertia: Measure of an object's resistance to angular acceleration; depends on mass distribution.

Compare rotational kinetic energy and translational kinetic energy.

Rotational Kinetic Energy: Kinetic energy due to rotational motion, $KE_{rot} = \frac{1}{2}I\omega^2$ . Translational Kinetic Energy: Kinetic energy due to translational motion, $KE_{trans} = \frac{1}{2}mv^2$ .

What is the effect of applying an external torque to a rotating object?

The object's angular momentum changes. The change is equal to the angular impulse imparted by the torque.

What happens if a spinning object's mass distribution changes, moving mass closer to the axis of rotation?

The moment of inertia decreases, and the angular speed increases to conserve angular momentum.

What is the effect of zero net external torque on a system?

The total angular momentum of the system remains constant.

What happens when a rotating object collides with a stationary object and they stick together?

The final angular velocity of the combined system will be lower than the initial angular velocity of the rotating object, due to the increased moment of inertia. Total angular momentum is conserved.

What is the effect of a figure skater pulling their arms inward during a spin?

Their moment of inertia decreases, causing their angular speed to increase, conserving angular momentum.

What happens when a spacecraft fires thrusters?

It creates an angular impulse, changing its rotational motion.