Centripetal Acceleration:

• In order for an object to execute circular motion - even at a constant speed - the object must be accelerating towards the center of rotation. This acceleration is called the centripetal or radial acceleration and has a magnitude of

Centripetal Force:

• The radial force needed to create this acceleration is call the centripetal force. It is directed towards the center of rotation and has a magnitude of

• For any object undergoing uniform circular motion, the net force towards the center of rotation must have a value equal the centripetal force.

Centrifugal Force:

• In a frame of reference rotating with an angular velocity w (omega), the object will be at rest, yet seem to experience a force acting upon it radially outwards equal to m w²r. This is because a rotating frame is a non-inertial frame of reference, i.e. the frame does not move at a constant speed in a straight line, and consequently Newton's First Law does not apply.

• It is sometimes useful to move into a frame that is rotating with the system. In this rotating frame, the centripetal force is replaced with a force of the same magnitude acting outwards, which is called the centrifugal force. ("Centrifugal" means "fleeing from the center.") In solving a problem in the rotating frame, the centrifugal force can be treated as though it were another physical force acting on the object with a magnitude m w²r (the same magnitude as the centripetal force) directed radially outwards. Most physicists would advise against doing this, because the centrifugal force is not a real force. I still find it useful in visualizing a problem.

Centripetal Force a Glass of Water Moving in a Vertical Circle Demo (430K)
A glass is partially filled with red colored water. The glass is then swung in a vertical circle. When the glass reaches the top of its arc will the water fall out?