Glossary
Angular Acceleration ($\alpha$)
The rate at which an object's angular velocity changes, indicating how quickly its rotation is speeding up or slowing down.
Example:
As a fan blade spins up from rest, it experiences a positive angular acceleration.
Angular Displacement ($ heta$)
The change in an object's angular position, representing how much it has rotated.
Example:
When a car tire completes half a turn, its angular displacement is radians.
Angular Momentum (L)
A measure of an object's rotational motion, dependent on its moment of inertia and angular velocity.
Example:
A spinning top maintains its upright position due to its angular momentum.
Angular Velocity ($\omega$)
The rate at which an object's angular position changes, indicating how fast it is rotating.
Example:
A spinning record player might have a constant angular velocity of 33.3 revolutions per minute.
Conservation of Angular Momentum
A fundamental principle stating that in a closed system with no external torques, the total angular momentum remains constant.
Example:
When a diver pulls their arms and legs in during a flip, their conservation of angular momentum causes them to spin faster.
Moment of Inertia (I)
A measure of an object's resistance to changes in its rotational motion, analogous to mass in linear motion.
Example:
A solid disk has a smaller moment of inertia than a hoop of the same mass and radius, making it easier to spin.
Newton's Second Law for Rotation
States that the net torque acting on an object is directly proportional to its angular acceleration and its moment of inertia ($\Sigma\tau = I\alpha$).
Example:
If you apply a larger net torque to a bicycle wheel, it will experience a greater angular acceleration.
Period (T)
The time it takes for an object to complete one full rotation or cycle.
Example:
The period of Earth's rotation on its axis is approximately 24 hours.
Radian
The standard unit for measuring angles in rotational motion, where one radian is the angle subtended by an arc equal in length to the radius.
Example:
A full circle is radians, which is approximately 6.28 radians.
Rotational Kinematics
The study of how things rotate, focusing on angular displacement, velocity, and acceleration without considering the causes of motion.
Example:
Calculating how far a Ferris wheel turns in a given time, knowing its constant angular speed, is a problem in rotational kinematics.
Rotational Kinetic Energy (K_rot)
The energy an object possesses due to its rotation.
Example:
A spinning flywheel stores rotational kinetic energy that can be used to power a device.
Torque ($ au$)
A twisting force that tends to cause rotation or change an object's rotational motion.
Example:
Applying a wrench to a stubborn bolt creates torque to loosen it.