Glossary
Angular momentum (L)
A measure of an object's rotational motion, calculated as L = r × p for a point particle or L = Iω for an extended object.
Example:
A spinning bicycle wheel possesses angular momentum, which helps stabilize the bike while riding.
Angular velocity (ω)
The rate at which an object rotates or revolves around an axis, typically measured in radians per second.
Example:
The angular velocity of a merry-go-round determines how fast children on it are spinning.
Ballistic Pendulum
A classic problem combining conservation of linear momentum during an inelastic collision with conservation of mechanical energy during the subsequent swing of the combined mass.
Example:
A ballistic pendulum experiment can be used to determine the speed of a bullet by measuring the maximum height the pendulum swings after the bullet embeds in it.
Conservation of Angular Momentum
The total angular momentum of a system remains constant unless acted upon by a net external torque.
Example:
When a figure skater pulls her arms in during a spin, her angular speed increases to maintain the Conservation of Angular Momentum for her system.
Conservation of energy (mechanical)
The principle that the total mechanical energy (kinetic plus potential) of a system remains constant if only conservative forces do work.
Example:
A roller coaster car speeding down a hill and then climbing another demonstrates the conservation of energy, converting potential to kinetic and back.
Conservation of momentum (linear)
The principle that the total linear momentum of an isolated system remains constant if no net external force acts on it.
Example:
When a rocket expels exhaust gases, the rocket moves forward due to the conservation of momentum between the rocket and the gases.
Disks Colliding
A common scenario in rotational dynamics where two or more rotating disks interact, conserving angular momentum because the torques between them are internal to the system.
Example:
In a demonstration, two disks colliding and sticking together on a frictionless axle illustrate how their combined angular velocity changes to conserve angular momentum.
Extended object
An object with a defined shape and size, for which angular momentum is calculated using its moment of inertia and angular velocity (L = Iω).
Example:
A spinning planet is an extended object whose angular momentum depends on its mass distribution and rotation rate.
Isolated system
A system upon which no net external torque acts, resulting in the conservation of its total angular momentum.
Example:
A satellite orbiting Earth, ignoring atmospheric drag, can be considered an isolated system for angular momentum.
Linear momentum (p)
A measure of an object's translational motion, calculated as the product of its mass and velocity (p = mv).
Example:
A heavy truck moving at high speed has a large linear momentum, making it difficult to stop quickly.
Moment of inertia (I)
A measure of an object's resistance to changes in its rotational motion, analogous to mass in linear motion.
Example:
A flywheel designed to store rotational energy needs a large moment of inertia to resist changes in its angular velocity.
Net external torque (τ)
The sum of all torques acting on a system from outside sources, which causes a change in the system's angular momentum.
Example:
Applying a wrench to a stubborn bolt creates a net external torque that causes the bolt to rotate.
Point particle
An idealized object with mass but no dimensions, for which angular momentum is calculated using its position vector, mass, and linear velocity (L = rmv sin(θ)).
Example:
When a small comet swings around a massive star, it can often be modeled as a point particle to simplify angular momentum calculations.
Rotational inertia
Another term for moment of inertia, representing an object's resistance to changes in its rotational motion.
Example:
A diver tucking into a ball reduces her rotational inertia, allowing her to complete multiple flips in the air.
Satellites
Objects orbiting a larger celestial body, where angular momentum is conserved, causing their orbital speed to change with their distance from the central body.
Example:
As Earth-orbiting satellites move closer to Earth, their orbital speed increases to conserve angular momentum.
Vector sum
The total angular momentum of a system is found by adding the individual angular momentum vectors of all its constituent parts.
Example:
To find the total angular momentum of a complex machine with multiple rotating parts, one must calculate the vector sum of each component's angular momentum.