Centripetal Force and Acceleration:
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
| ac |
= Centripetal acceleration |
SI: m/s2 |
vT
|
= Tangential velocity or speed |
SI: m/s |
r
|
= Radius of object's path |
SI: m |
w
|
= Angular velocity |
SI: rad/s |
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 ω (omega), the object will be at rest, yet seem to experience a force acting upon it radially outwards equal to m ω2r.
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 ω2r (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.