8.3 - Centripetal acceleration

Centripetal acceleration: The centrally directed

acceleration of an object due to its circular

motion.

An object moving in uniform circular motion constantly accelerates because its direction

(and therefore its velocity) constantly changes. This type of acceleration is called

centripetal acceleration. Any object moving along a circular path has centripetal

acceleration.

In Concept 1 at the right is a vector analysis of centripetal acceleration that uses a toy

train as an example of an object moving along a circular path. As the drawing indicates,

the train’s velocity is tangent to the circle.

In uniform circular motion, the acceleration vector always points toward the center of the

circle, perpendicular to the velocity vector. In other words, the object accelerates toward

the center. This can be proven by considering the change in the velocity vector over a

short period of time and using a geometric argument (an argument that is not shown

here).

The equation for calculating centripetal acceleration is shown in Equation 1 on the right.

The magnitude of centripetal acceleration equals the speed squared divided by the

radius. Since both the speed and the radius are constant in uniform circular motion, the

magnitude of the centripetal acceleration is also constant.

With uniform circular motion, the only acceleration is centripetal acceleration, but for

circular motion in general, there may be both centripetal acceleration, which changes

the object’s direction, and acceleration in the direction of the object’s motion (tangential

acceleration), which changes its speed. If you ride on a Ferris wheel which is starting

up, rotating faster and faster, you are experiencing both centripetal and tangential

acceleration. For now, we focus on uniform circular motion and centripetal acceleration,

leaving tangential acceleration as another topic.

Centripetal acceleration

Acceleration due to change in direction

in circular motion

In uniform circular motion, acceleration:

·Has constant magnitude

·Points toward center

ac = centripetal acceleration

v = speed

r = radius

What is the centripetal

acceleration of the train?

Accelerates toward center

(^168) Copyright 2000-2007 Kinetic Books Co. Chapter 08