Centripetal Acceleration and Circular Motion Circular Motion B

Centripetal Acceleration and Circular Motion

Circular Motion B A C v Answer: B 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 v 2 R R v 1 centripetal acceleration Acceleration is due to change in direction, not speed. Since turns “toward” center, must be a force toward center. 12

Acceleration in Uniform Circular Motion Draw in forces. v 1 12

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

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

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

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 FN exerted on you by the car seat as you drive past the bottom of the hill A. FN < mg a=v 2/R B. FN = mg C. FN > mg R correct FN v mg 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. Y Direction: F = ma N Let N = 0, just touching mg 25

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