Circular Motion

AP PhysicsMrs Coyle

•Earth rotates about its axis

•Satellite revolves about

the earth.

Rotation vs Revolution

Uniform Circular Motion

Linear(tangential)speed, v, is constant.

-Tangential Velocity-Centripetal Acceleration

v

v

-The tangential velocity vector is tangent to the circle at the point of study.v= 2r/T = 2rf = d/t

-Centripetal Acceleration: points to center

a= v2 / r

How does the v vary with r?

The linear speed increases as r increases.

Example: How does your linear speed change

when you are on a merry-go-round and you move away from the center?

How does the f vary with r? f does not depend on r

Example: How does your frequency change

when you are on a merry-go-round and you move away from the center?

Centripetal Force, Fc= m v2

r Is a center seeking force. (Always

points to the center.) Is perpendicular to the tangential

velocity at any given instant.

It is not an extra force. It is an existing force(s) that point(s) to the center.

What force represent s the centripetal force for a coin on a record player?

What force plays the role of the centripetal force when a car rounds a curve?

Car Rounding a Bend (Flat Road)

Example 1: Car Rounding a Curve

A car is travelling with a speed of 45km/h on a circular horizontal track of radius 50m. What is the minimum coefficient of friction, so that the car stays on the track?

Answer: 0.3

Rotor Ride

Rotor Ride http://www.youtube.com/watch?v=J7k

8Oz_73mw&feature=player_embedded#

What force plays the role of the centripetal force in the rotor ride?

http://upload.wikimedia.org/wikipedia/commons/7/7d/Rotormidcyclelunapraksyd.JPG

Example 2: Rotor A brave student rides in a rotor of radius

5m whose floor drops when it reaches a speed of 20mi/h. What is the coefficient of friction between the student and the wall of the rotor, so that the student does not fall?

Answer: 0.6

What forces represent the centripetal force for a child on this ride?

Example 3 Conical Pendulum

Find an expression for v in terms of L and

Ans: v=√Lgsin tan

Can be 90o for a conical pendulum? (Can there be a horizontal circular path when twirling a ball)?

Example 4 Car on a banked road

At what angle should the road be banked if a car is to safely round the curve at a speed of 13.4 m/s and the radius of the curve is 50m if friction is neglected?

Ans: 20.1o

Non-Uniform Circular Motion v tangential is not constant.

There are both tangential and radial accelerations and therefore forces.

What force plays the role of the centripetal force when a ball is on the top of a loop-the-loop?

Loop the Loop

Example 5: Loop-the-loop What is the critical velocity of a ball

at the top of the loop of radius .3m so that it completes the loop?

Answer: 1.7m/s