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 $\vec{L} = \vec{r} \times \vec{p}$ .

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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 key difference between angular momentum and linear momentum?

Angular momentum is for rotational motion, while linear momentum is for straight-line motion. Both are conserved, but under different conditions.

Compare the effects of internal vs. external forces on angular momentum.

Internal forces do not change the total angular momentum of a system. External forces (torques) are required to change the total angular momentum.

Compare a system with zero external torque and a system with nonzero external torque in terms of angular momentum.

Zero external torque: Angular momentum is conserved and remains constant. Nonzero external torque: Angular momentum changes due to angular impulse from the torque.

Compare the roles of moment of inertia and angular velocity in determining angular momentum.

Moment of inertia (I) is the resistance to rotational change, while angular velocity (ω) is the rate of rotation. Angular momentum (L) is the product of these two: L = Iω.

Compare rigid and non-rigid systems in the context of angular momentum.

Rigid system: Moment of inertia is constant unless external forces act. Non-rigid system: Moment of inertia can change due to changes in shape or mass distribution, affecting angular speed.

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

Sum the individual angular momentum vectors of each part of the system, considering both magnitude and direction.

How does a figure skater use conservation of angular momentum?

By changing their moment of inertia (e.g., pulling arms in), they alter their angular speed to conserve angular momentum.

What happens to angular speed when moment of inertia decreases, assuming constant angular momentum?

Angular speed increases.

Describe the process of angular momentum transfer.

If the net external torque on a system is nonzero, angular momentum is transferred between the system and its environment. The change in angular momentum equals the angular impulse from the net external torque over a time interval.

How do you determine if angular momentum is conserved in a system?

Check if the net external torque acting on the system is zero. If it is, angular momentum is conserved.

Describe the steps to solve a problem involving conservation of angular momentum.

Identify the system. 2. Check for external torques. 3. If no external torques, apply conservation of angular momentum: L_initial = L_final. 4. Solve for the unknown variables.