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 |
- 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.
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