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Define conservation of angular momentum.
The total angular momentum of a closed system remains constant unless acted upon by an external torque.
What is angular impulse?
Angular impulse is 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 rotation rate. It depends on the mass distribution of the object and the axis of rotation.
What is a closed system in the context of angular momentum?
A system where no external torques act upon it, allowing angular momentum to be conserved.
Define angular momentum.
The rotational equivalent of linear momentum. For a point particle, it is given by $\vec{L} = \vec{r} \times \vec{p}$, where $\vec{r}$ is the position vector and $\vec{p}$ is the linear momentum.
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 angular momentum?
The rotational equivalent of linear momentum; a measure of an object's resistance to change in its rotation.
Define moment of inertia.
A measure of an object's resistance to changes in its rotational speed about an axis of rotation. It depends on the mass and the distribution of mass relative to the axis.
What is torque?
A twisting force that tends to cause rotation. It is the rotational equivalent of linear force.
Define angular impulse.
The change in angular momentum of an object. It is equal to the net external torque multiplied by the time interval over which the torque acts.
What is net external torque?
The sum of all torques acting on a system due to forces external to the system.
Define angular velocity.
The rate of change of angular displacement with respect to time, typically expressed in radians per second.