Angular to Linear Acceleration Equation
Reference from the original Physics I textbook.
- Angular to Linear Acceleration Equation
Tangential acceleration magnitude: a_t = r|α|. For signed tangential components, a_t = rα.
Vector form: a⃗_t = α⃗ × r⃗. The radial acceleration is a_c = rω² and must be included when finding total linear acceleration.
- Related Glossary Terms
Angular Accelerationⓘ, Angular to Linear Velocity Equation, Angular Velocity↗
- Index
Reviewed physics notes (2)
These corrections keep the original lesson’s purpose while fixing errors in the source edition.
- Source makes the tangential acceleration vector parallel to the angular-acceleration axis vector. — Reference 1
- Original a/r gives only the tangential relation, not total acceleration. — Reference 1
Glossary and deeper reading · 3 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
-
Acceleration
Acceleration is the vector rate of change of velocity with time. It can change an object’s speed, direction, or both, and it is measured in meters per second squared. For example, a satellite moving at constant speed in a circular orbit accelerates toward the center.
-
Angular acceleration
Angular acceleration is the rate of change of angular velocity. For a fixed axis its sign follows the chosen positive rotation direction, and its units are radians per second squared. For example, a fan speeding up has angular acceleration, whereas one turning steadily does not.
-
Angular velocity
Angular velocity describes the rate and direction of rotation about an axis. For a fixed axis, a signed angular velocity is measured in radians per second, while its magnitude is angular speed. For example, points on one rigid turntable share the same angular speed even though outer points have greater linear speeds.