Dynamics of Uniform Circular Motion

We know from a previous lesson that uniform circular motion is motion of an object in a circle at a constant speed. Since Newton's First Law states that an object in motion will remain in motion at a constant speed and
traveling in a straight line unless an external force acts upon it, there must be some external force that causes uniform circular motion. In fact, this force could be any of a number of forces, such as a string pulling on a ball, the friction of your car tires against the road in a turn, or gravity pulling on a satellite. We call any such force that directs the acceleration towards the center of a circular path Centripetal Force.

- All forces acting upon an object when it is moving in a circular motion are known as centripetal forces. Centripetal Force means Center Seeking Force.

- Centrifugal force is often spoken of though it doesn’t exist. It is thought of as a “center fleeing” force. However there is not a net force applied toward the outside of a circle when an object is moving around it in Uniform Circular Motion. Want more? Try The Forbidden F-Word

We can apply some math to the situation to come up with a net force equation for objects in uniform circular motion. Recall Newton's Second Law:

Since centripetal acceleration (ac) is given by the formula

then substituting, Centripetal Force is given by the equation:

Here are some more links with examples and explanations on Centripetal Acceleration and Circular Motion:

http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html

http://www.physicsclassroom.com/mmedia/circmot/cf.html

The NTNU Virtual Physics Laboratory provides several
excellent applets that demonstrate principles of Physics. Click here for an applet on
Uniform Circular Motion.

For Practice Problems, Try:

From The Physics Classroom:

http://www.physicsclassroom.com/Class/circles/U6L1c.html

http://www.physicsclassroom.com/Class/circles/U6L1e.html

From the University of Oregon:

A child on a swing

Rollercoaster loop

Tetherball

Giancoli Multiple Choice Practice Questions (Select "Practice Problems) and try some. Don't worry - you won't be able to do all of them yet.