Unit 5: Angular Momentum & Conservation Laws

Angular Momentum (L)

A measure of the intensity of rotational motion, defined as the cross product of position vector and linear momentum.

Point Particle

An object with mass that does not necessarily have to be spinning to possess angular momentum.

Cross Product

A mathematical operation that finds a vector perpendicular to two given vectors.

Lever Arm (r_{})

The distance from the axis of rotation to the point of application of force, used to determine torque and angular momentum.

Moment of Inertia (I)

A scalar value representing an object's resistance to changes in its rotational motion.

Angular Velocity (7)

The rate of change of angular displacement, often expressed in radians per second.

Conservation of Angular Momentum

The principle stating that if no external torque acts on a system, its total angular momentum remains constant.

Torque ()

A measure of the force that produces or changes rotational motion.

Net External Torque

The total torque resulting from all external forces acting on a system.

Mass (m)

The amount of matter in an object, which influences its inertia and angular momentum.

Velocity (v)

The speed of an object in a specified direction.

Cross Product Formula

 =  imes .

Relation of Angular Momentum to Torque

 =   rac{d}{dt}.

Rotational Kinetic Energy

The energy of an object due to its rotation, given by the formula  = rac{1}{2} I ^{2}.

Angular Momentum of a Rigid Body Formula

 = I .

Ice Skater Effect

A phenomenon where a skater can increase their angular velocity by pulling in their arms.

Rotational Collisions

Collisions that involve rotating bodies, where angular momentum is often conserved even if linear momentum is not.

Perpendicular Distance

The shortest distance from the line of action of a force to the axis of rotation.

System of Particles

A collection of particles, which can be analyzed for their overall properties like momentum and angular momentum.

Final Angular Momentum

The total angular momentum of a system after an interaction, based on conservation principles.

Angular Momentum Relative to a Pivot

The angular momentum calculated from the position and velocity of a particle according to a specific pivot point.

Conservation Principles

Laws stating that certain quantities (like energy or angular momentum) remain constant in isolated systems.

Impact of External Forces

The effect of forces acting outside a system, which can change the system's momentum behavior.

Collisions and Angular Momentum

In collisions involving rotating bodies, angular momentum is conserved about the pivot point if no net external torque acts.

Velocity Vector (v)

A vector quantity that has both magnitude and direction, describing an object's motion.

Calculating Angular Momentum

Use  = mvr ( heta) for magnitude, where r is the distance from pivot to mass.