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What is Angular Momentum (L) for a point particle?
$L = r \times p = r m v \sin(\theta)$
What is Angular Momentum (L) for an extended object?
$L = I \omega$
Define Conservation of Angular Momentum.
The total angular momentum of a system remains constant unless acted upon by a net external torque.
What is the relationship between torque and angular momentum?
$\tau = \frac{dL}{dt}$
Define moment of inertia.
A measure of an object's resistance to changes in its rotation.
What is torque?
A rotational force that causes a change in angular momentum.
What is the effect of applying a net external torque on a system?
The angular momentum of the system changes, as described by $\tau = \frac{dL}{dt}$.
What happens to a satellite's speed as it moves closer to a planet?
Its speed increases to conserve angular momentum.
What happens when a figure skater pulls their arms inward during a spin?
Their moment of inertia decreases, and their angular speed increases to conserve angular momentum.
What is the effect of a bullet embedding itself in a block in a ballistic pendulum?
The block and bullet system gains momentum, and the system begins to swing upwards.
What happens if the moment of inertia of a rotating object decreases?
The angular velocity must increase to conserve angular momentum, assuming no external torque.
What are the key differences between linear and angular momentum?
Linear Momentum: $p=mv$, translational motion | Angular Momentum: $L=I\omega$, rotational motion
Differentiate between elastic and inelastic collisions in the context of angular momentum.
Elastic: Kinetic energy is conserved, Angular momentum is conserved | Inelastic: Kinetic energy is not conserved, Angular momentum is conserved