Centripetal Acceleration and Circular Motion

A B C Answer: B v Circular Motion A ball is going around in a circle attached to a string. If the string breaks at the instant shown, which path will the ball follow? 10

Acceleration in Uniform Circular Motion vv2vv2 vv1vv1 R RRRR centripetal acceleration 12 Acceleration is due to change in direction, not speed. Since turns “toward” center, must be a force toward center.

Acceleration in Uniform Circular Motion vv1vv1 12 Draw in forces.

Common Incorrect Forces Acceleration:  F = ma l Force of Motion (Inertia not a force) l Centrifugal Force (wrong object!) l Centripetal Force (tension, gravity, friction, normal)

Example: ball in vertical circle v v 1 =10m/s 12 Draw in forces. A ball of mass 2kg is being swung in a vertical circle with a speed of 10m/s. What is the tension in the rope at the top of the circle? g

Example: ball in vertical circle v v 1 =10m/s 12 Draw in forces. A ball of mass 2kg is being swung in a vertical circle with a speed of 10m/s. What is the tension in the rope at the bottom of the circle? g

Example Suppose you are driving through a valley whose bottom has a circular shape. If your mass is m, what is the magnitude of the normal force F N exerted on you by the car seat as you drive past the bottom of the hill A. F N mg v mg FNFN R a=v 2 /R correct 20

Example: roller coaster What is the minimum speed you must have at the top of a 20 meter roller coaster loop, to keep the wheels on the track. 25 mg N Y Direction: F = ma Let N = 0, just touching

Summary of Concepts l Uniform Circular Motion è Speed is constant è Direction is changing è Acceleration toward center a = v 2 / r è Newton’s Second Law F = ma 50