Linear velocity and angular velocity both describe how fast something moves, but they measure different kinds of motion. Linear velocity is the rate at which a point changes position, such as the speed of a runner's center of mass or a barbell, and is usually reported in meters per second. Angular velocity is the rate at which an angle or orientation changes, such as how fast the knee extends or the trunk rotates, and is reported in degrees or radians per second. Both are vectors, meaning they include a direction as well as a magnitude.
When to use each
- Use linear velocity for questions about how fast the body, an implement, or a ball travels: sprint speed, bar velocity, or release speed.
- Use angular velocity for questions about rotation and joint motion: hip rotation in a swing, knee extension in a kick, or shoulder rotation in a throw.
- Use both together to study sequencing, where rotating segments contribute to the linear speed of a distal point such as the hand, foot, or club head.
How to see it on video
Both are calculated from changes between frames divided by the time between those frames, so the frame rate must be known. Linear velocity also requires calibration against a known distance in the plane of movement. Angular velocity does not need a distance reference, but the measured angles are only reliable when the camera is reasonably perpendicular to the plane of rotation. Fast movements need a high frame rate and a fast shutter speed so that consecutive positions are sharp and closely spaced.
Common mix-ups
- For a point on a rotating segment, linear velocity equals angular velocity multiplied by the distance from the axis, with angular velocity in radians per second. A longer lever produces more linear speed at the same rotation rate.
- Speed and velocity are not identical. Speed is the magnitude only, while velocity includes direction.
- Joint angular velocity describes how fast one segment moves relative to another. It differs from a segment's angular velocity relative to the ground or camera.
Choosing the right one depends on whether the coaching question is about travel or rotation.