Glossary
Angular Impulse
The product of the net external torque acting on a system and the time interval over which it acts, resulting in a change in the system's angular momentum.
Example:
A gymnast pushing off a high bar to initiate a flip applies an Angular Impulse to their body, changing their rotational state.
Angular Impulse
The product of the net torque acting on an object and the time interval over which it acts, resulting in a change in the object's angular momentum.
Example:
A brief, strong push on a merry-go-round applies an angular impulse, causing it to spin faster.
Angular Momentum (L)
A measure of the quantity of rotational motion an object possesses, calculated as the product of its moment of inertia and angular velocity (L = Iω).
Example:
A planet orbiting the sun possesses Angular Momentum due to its orbital motion, which remains constant in the absence of external torques.
Angular Speed (ω)
The rate at which an object rotates or revolves, measured as the angular displacement per unit time.
Example:
A car tire spinning at 100 radians per second has a high angular speed.
Angular Velocity (ω)
The rate at which an object rotates or revolves, measured in radians per second, indicating both speed and direction of rotation.
Example:
A record spinning at 33 1/3 revolutions per minute has a specific Angular Velocity that determines how fast the music plays.
Closed Systems (Angular Momentum)
A system where no net external torques act upon it, leading to the conservation of its total angular momentum.
Example:
A satellite orbiting Earth can be approximated as a closed system for angular momentum, as gravitational forces are internal to the Earth-satellite system.
Conservation of Angular Momentum
A fundamental principle stating that the total angular momentum of a system remains constant if no net external torque acts on it.
Example:
A spinning ice skater pulls their arms in, and their angular speed increases, demonstrating the Conservation of Angular Momentum as their moment of inertia decreases.
Conservation of Angular Momentum
States that the total angular momentum of a closed system remains constant unless acted upon by an external torque. It is the rotational equivalent of linear momentum conservation.
Example:
A figure skater pulling their arms in demonstrates the conservation of angular momentum, as their angular speed increases while their total angular momentum remains constant.
External Interaction
Any influence originating from outside a defined system that causes a change in the system's total angular momentum.
Example:
When a child pushes a spinning merry-go-round, the push is an External Interaction that changes the merry-go-round's angular momentum.
External Torques
Torques originating from outside a defined system that can cause a change in the system's total angular momentum.
Example:
Applying a brake to a spinning bicycle wheel creates an external torque that slows down its rotation.
Impulse-Momentum Theorem (Angular)
States that the change in an object's angular momentum is equal to the net angular impulse applied to it.
Example:
If a constant torque acts on a flywheel for a specific duration, the Impulse-Momentum Theorem (Angular) can be used to calculate its final angular velocity.
Linear Momentum
A measure of the quantity of motion of an object in a straight line, calculated as the product of its mass and velocity.
Example:
A bowling ball rolling down the lane has Linear Momentum that carries it towards the pins.
Mass Distribution
Refers to how the mass of an object is arranged or spread out relative to its axis of rotation, directly influencing its moment of inertia.
Example:
When a spinning ice skater pulls their arms in, they change their mass distribution, decreasing their moment of inertia and increasing their angular speed.
Moment of Inertia (I)
A measure of an object's resistance to changes in its rotational motion, analogous to mass in linear motion. It depends on the mass distribution relative to the axis of rotation.
Example:
A long, thin pole has a higher Moment of Inertia when rotated about its center than a compact sphere of the same mass, making it harder to spin.
Moment of Inertia (I)
A measure of an object's resistance to changes in its rotational motion, analogous to mass in linear motion. It depends on the object's mass and its distribution relative to the axis of rotation.
Example:
A long, thin rod has a larger moment of inertia when rotated about its end compared to its center, making it harder to start or stop spinning.
Net External Torque
The vector sum of all torques acting on a system from outside its defined boundaries. If this sum is zero, angular momentum is conserved.
Example:
If a bicycle wheel is spinning freely on its axle, the Net External Torque acting on it is zero, allowing it to maintain its angular momentum.
Non-Rigid Systems
Systems whose mass distribution can change, allowing for alterations in angular speed without a change in total angular momentum.
Example:
A diver tucking into a ball mid-air is an example of a non-rigid system, as they change their body shape to increase their rotational speed.
Rotational Kinetic Energy
The kinetic energy an object possesses due to its rotation, calculated as half the product of its moment of inertia and the square of its angular speed.
Example:
A heavy flywheel spinning rapidly stores a significant amount of rotational kinetic energy, which can be used to power machinery.
Torque
A rotational force that causes or tends to cause rotation or a change in rotational motion. It is the rotational equivalent of linear force.
Example:
Applying a wrench to a stubborn bolt creates Torque, which can cause the bolt to rotate and loosen.
Total Angular Momentum
The vector sum of the individual angular momenta of all parts within a defined system.
Example:
For a complex machine with multiple rotating gears, the Total Angular Momentum is found by adding the angular momentum of each gear, considering both their speed and direction of rotation.
Total Angular Momentum
The sum of the angular momenta of all individual components or parts within a system.
Example:
To find the total angular momentum of a spinning planet with a moon orbiting it, you would add the angular momentum of the planet's spin to the angular momentum of the moon's orbit.