Glossary
Acceleration (a)
The rate of change of an object's linear velocity, indicating how quickly its speed or direction is changing, measured in meters per second squared (m/s²).
Example:
When a rocket launches, it experiences a large upward *.
Angular Acceleration (α)
The rate at which an object's angular velocity changes, indicating how quickly its rotation speed is increasing or decreasing, measured in radians per second squared (rad/s²).
Example:
When a car's engine revs up, the crankshaft experiences a significant *.
Angular Position (Δθ)
The angular displacement, which is the change in the angle of a rotating object from a reference point, typically measured in radians.
Example:
If a door opens 90 degrees, its * is π/2 radians.
Angular Velocity (ω)
The rate at which an object's angular position changes, indicating how fast an object is rotating, measured in radians per second (rad/s).
Example:
A spinning bicycle wheel has a specific * that determines how quickly it completes revolutions.
Arc Length (Δx = rΔθ)
The linear distance traveled along the circumference of a circle due to an angular displacement, connecting linear and rotational motion.
Example:
The distance a point on the edge of a spinning merry-go-round travels is its *.
Displacement (Δx)
The change in linear position of an object, representing the straight-line distance and direction from its initial to its final point, measured in meters.
Example:
If a ball rolls 3 meters to the right, its * is +3 meters.
Linear Acceleration (a = rα)
The tangential acceleration of a point on a rotating object, directly proportional to its angular acceleration and its distance from the axis of rotation.
Example:
As a car's wheels spin faster, a point on the tire's tread experiences a significant *.
Linear Velocity (v = rω)
The tangential speed of a point on a rotating object, directly proportional to its angular velocity and its distance from the axis of rotation.
Example:
The tip of a propeller blade has a much greater * than a point near its hub.
Rolling without slipping
A condition where an object rotates and translates simultaneously such that the point of contact with the surface has zero instantaneous velocity, implying a direct relationship between linear and angular motion.
Example:
A bowling ball moving down the lane perfectly, with its rotation matching its forward speed, is an example of *.
Rotational Kinematics
The branch of mechanics that describes the motion of rotating objects using concepts like angular position, angular velocity, and angular acceleration, without considering the forces causing the motion.
Example:
When analyzing how a spinning figure skater changes their rotation speed, you are studying *.
Rotational Motion
The movement of an object around a fixed axis, where all points on the object trace out circular paths.
Example:
A ceiling fan blades exhibit * as they spin around the central motor.
Translational Motion
The motion of an object along a straight or curved path, where all points on the object move in the same direction and at the same rate.
Example:
A car driving in a straight line down a road is undergoing pure *.
Velocity (v)
The rate of change of an object's linear position, indicating both its speed and direction, measured in meters per second (m/s).
Example:
A runner completing a 100-meter dash has a high average *.