Centripetal acceleration

Definition

Centripetal acceleration is the acceleration experienced by an object moving in a circular path, directed towards the center of the circle. It is responsible for changing the direction of the object's velocity without altering its speed.

5 Must Know Facts For Your Next Test

1. Centripetal acceleration is given by $a_c = \frac{v^2}{r}$, where $v$ is the tangential velocity and $r$ is the radius of the circular path.
2. It always points towards the center of the circle, perpendicular to the tangential velocity.
3. The centripetal force causing this acceleration can be due to gravity, tension, friction, or other forces depending on the situation.
4. If either the speed of the object or the radius of its path changes, so does its centripetal acceleration.
5. $a_c$ can also be expressed in terms of angular velocity $\omega$ as $a_c = r\omega^2$.

Review Questions

• What is centripetal acceleration and how does it affect an object's motion?
• How do you calculate centripetal acceleration using tangential velocity and radius?
• Describe a scenario where tension provides the centripetal force needed for circular motion.

Related terms

Tangential Velocity: The linear speed of an object moving along a circular path, measured at any point tangent to that path.

Centripetal Force: The net force causing centripetal acceleration, directed towards the center of circular motion.

Angular Velocity: $\omega$, a measure of how quickly an object rotates or revolves relative to another point; often measured in radians per second.