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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, $KE_{trans} = \frac{1}{2}mv^2$.
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.
What is angular momentum?
The rotational equivalent of linear momentum. It's conserved in a closed system unless acted upon by an external torque.
What is the conservation of angular momentum?
The total angular momentum of a closed system remains constant if no external torque acts on it.
Define external torque.
A torque applied from outside the system that can change the system's total angular momentum.
What is angular impulse?
The product of the net torque and the time interval over which it acts. Units are $\text{kg} \cdot \text{m}^2/\text{s}$.
Define moment of inertia.
A measure of an object's resistance to changes in its rotational motion. Analogous to mass in linear motion.