Total linear acceleration

Definition

Total linear acceleration is the vector sum of tangential and centripetal accelerations in a rotating system. It describes the overall linear acceleration experienced by a point on a rotating object.

5 Must Know Facts For Your Next Test

1. Total linear acceleration combines both tangential acceleration ($a_t$) and centripetal acceleration ($a_c$).
2. Tangential acceleration ($a_t$) is given by $a_t = \alpha r$, where $\alpha$ is angular acceleration and $r$ is the radius.
3. Centripetal acceleration ($a_c$) is calculated using $a_c = \omega^2 r$, where $\omega$ is angular velocity.
4. The magnitude of total linear acceleration can be found using the Pythagorean theorem: $a = \sqrt{a_t^2 + a_c^2}$.
5. Total linear acceleration points in the direction of the net force acting on the point in question.

Review Questions

• What are the components that make up total linear acceleration?
• How do you calculate tangential and centripetal accelerations?
• What formula would you use to determine the magnitude of total linear acceleration?

Related terms

Tangential Acceleration:

The rate of change of tangential velocity, given by $a_t = \alpha r$.

Centripetal Acceleration:

The inward-directed acceleration that keeps an object moving in a circular path, calculated as $a_c = \omega^2 r$.

Angular Velocity:

The rate at which an object rotates or revolves, denoted as $\omega$, usually measured in radians per second.