Glossary
Acceleration
The rate at which an object's velocity changes over time.
Example:
When a rocket launches, its acceleration is immense, rapidly increasing its speed.
Angular Acceleration (α)
The rate of change of angular velocity, indicating how quickly an object's rotation speed is changing, measured in rad/s².
Example:
When a bicycle wheel starts from rest and speeds up, it experiences angular acceleration.
Angular Displacement (Δθ)
The change in the angular position of a rotating object, measured in radians.
Example:
If a Ferris wheel rotates half a turn, its angular displacement is π radians.
Angular Velocity (ω)
The rate of change of angular displacement, indicating how fast an object is rotating, measured in rad/s.
Example:
A spinning top with a high angular velocity completes many rotations per second.
Arc Length (s)
The distance along the circumference of a circle, calculated as the product of the radius and the angular displacement in radians.
Example:
If a car tire with a 0.3m radius rotates by 10 radians, the arc length traveled by a point on its edge is 3 meters.
Clockwise (CW)
The direction of rotation matching the movement of clock hands, conventionally considered the negative direction in rotational motion.
Example:
Tightening a screw usually involves turning it clockwise.
Counterclockwise (CCW)
The direction of rotation opposite to the movement of clock hands, conventionally considered the positive direction in rotational motion.
Example:
When you loosen a screw, you typically turn it counterclockwise.
Displacement
The change in an object's position, including both magnitude and direction.
Example:
If you walk 5 meters east and then 5 meters west, your total displacement is zero, even though you walked 10 meters.
Distance
The total path length traveled by an object, regardless of direction.
Example:
Running a full lap around a 400-meter track means you covered a distance of 400 meters.
Inertial Reference Frame
A reference frame where an object at rest stays at rest, and an object in motion stays in motion with constant velocity, unless acted upon by a net force.
Example:
When you're riding in a car at a constant speed on a straight road, your body feels like it's in an inertial reference frame because you don't feel pushed or pulled unless the car accelerates.
Linear Acceleration (a)
The tangential acceleration of a point on a rotating object, calculated as the product of the radius and the angular acceleration.
Example:
As a merry-go-round speeds up, a child on its edge experiences linear acceleration in the direction of their motion.
Linear Velocity (v)
The tangential speed of a point on a rotating object, calculated as the product of the radius and the angular velocity.
Example:
A point on the edge of a spinning record has a greater linear velocity than a point closer to the center.
Period (T)
The time it takes for one complete revolution or cycle of rotation.
Example:
The period of Earth's rotation around its axis is approximately 24 hours.
Position
The location of an object relative to a reference point.
Example:
To describe where a car is, you might state its position as 50 meters east of the school.
Radian
A unit of angular measurement where one radian is the angle subtended at the center of a circle by an arc equal in length to the radius.
Example:
A full circle measures 2π radians, which is approximately 6.28 radians.
Rotational Kinematics Equations
A set of equations used to describe rotational motion with constant angular acceleration, analogous to linear kinematics equations.
Example:
You can use rotational kinematics equations to predict how long it takes a spinning wheel to stop if you know its initial angular velocity and constant angular deceleration.
Speed
The magnitude of velocity, representing how fast an object is moving without regard to direction.
Example:
A speedometer in a car measures its speed, not its velocity.
Velocity
The rate at which an object changes its position, a vector quantity including both speed and direction.
Example:
A car traveling at 60 km/h north has a different velocity than a car traveling at 60 km/h south.