Tuesday, May 27, 2008

Collected Circular Motion Lab Reports

Uniform circular motion - Motion in a circle at constant (uniform) speed.

Showed using definition of acceleration, a = (vf-vi)/t and adding the vectors using the parallelogram rule that for uniform circular motion, the acceleration is directed towards the center of circle.

Since there is an acceleration directed towards the center of the circle, and F = m*a, there must be a force also directed towards the center of the circle. The acceleration is ALWAYS in the direction of the net force. There must be an acceleration since the direction of velocity always changes even though the speed is constant. Since the force is perpendicular to the direction of motion, the direction changes even though the speed remains constant.

When the acceleration and force are directed towards the center of the circle, they are called the centripetal acceleration and centripetal force. Centripetal means "center seeking". This is not to be confused with centrifugal which is a "dirty" word in physics and should not be used. There is no such thing as a centrifugal force - this is only what you feel due to inertia.

Showed using octagons that F ~ 1/R, and F ~ v^2.
The complete equation is F = m * v^2/R

In solving problems, you always choose one axis in the direction of the acceleration which is towards the center of the circle. Find the sum of the forces in the radial direction and, instead of setting it equal to m * a, draw a little lightning bolt, write the word "zap", and set the sum equal to m * v^2/R. We "Zap" it because we didn't actually derive the equation, just pulled it out of thin air.

Note that m * v^2/R has the units of mass * acceleration. It is the centripetal force. v^2/R is the centripetal acceleration.

There must always be something physical that you can name as the centripetal force. Never just write down a centripetal force without identifying what causes it.

Gave several examples of centripetal force and solved several problems using uniform circular motion.

Handed out RA 7.4 for homework due tomorrow.
Also handed out problem sheet on circular motion. The front side is for practice. The three problems on the back are for extra credit if handed in by Friday.