Glossary
Angular Displacement (θ)
The angle, measured in radians, through which an object rotates around a fixed axis. It represents the change in an object's angular position.
Example:
When a clock's minute hand moves from 12 to 3, its angular displacement is π/2 radians.
Angular quantities
Physical measurements used to describe rotational motion, including angular displacement, angular velocity, and angular acceleration, which have direct analogies to linear motion concepts.
Example:
Understanding the relationship between angular quantities and their linear counterparts allows you to calculate the tangential speed of a point on the edge of a rotating wheel.
Average Angular Acceleration (αavg)
The rate at which an object's angular velocity changes over a specific time interval, calculated as the change in angular velocity divided by the time taken.
Example:
A car engine revving up from idle to high RPMs experiences a significant average angular acceleration of its crankshaft.
Average Angular Velocity (ωavg)
The rate at which an object's angular position changes over a specific time interval, calculated as the total angular displacement divided by the time taken.
Example:
If a ceiling fan completes 10 rotations (20π radians) in 5 seconds, its average angular velocity is 4π rad/s.
Radians
The standard SI unit for measuring angles, particularly in rotational motion. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius.
Example:
To correctly use rotational kinematic equations, all angular measurements, like 360 degrees, must first be converted to radians (2π radians).
Radians per second (rad/s)
The standard SI unit for measuring angular velocity, indicating the number of radians an object rotates through per second.
Example:
A high-speed blender might have a blade rotating at thousands of radians per second.
Radians per second squared (rad/s²)
The standard SI unit for measuring angular acceleration, representing the change in angular velocity (in rad/s) per second.
Example:
When a spinning top slows down due to friction, its angular acceleration is a negative value measured in radians per second squared.
Rigid systems
Objects or collections of particles that maintain a fixed shape and size during rotation, meaning all points within the system rotate with the same angular velocity.
Example:
A spinning bicycle wheel can be modeled as a rigid system because all its spokes and rim rotate together.
Rotational Kinematics
The branch of physics that describes the motion of objects rotating around an axis, using angular measurements and analogous concepts to linear kinematics.
Example:
Understanding rotational kinematics is essential for analyzing how a spinning merry-go-round accelerates or decelerates.
Rotational Kinematics Equations
A set of mathematical formulas that relate angular displacement, initial and final angular velocities, angular acceleration, and time for objects undergoing constant angular acceleration.
Example:
Using the rotational kinematics equations, you can determine how long it takes for a spinning flywheel to stop if you know its initial angular velocity and constant deceleration.