Centripetal Acceleration and Centripetal Acceleration and Circular Motion Circular Motion

A

B

C

Answer: B

v

Circular MotionCircular 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 Acceleration in Uniform Circular MotionCircular Motion

vv2

vv1RRRR

avR

2

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 Acceleration in Uniform Circular MotionCircular Motion

vv1

12

Draw in forces.

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

normal)

Example: Example: ball in vertical circleball in vertical circle

vv1=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: Example: ball in vertical circleball in vertical circle

vv1=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

ExampleExampleSuppose 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 B. FN = mg C. FN > mg

v

mg

FN

R

a=v2/R

correct

20

Example: roller Example: roller coastercoaster

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

mgN

Y Direction: F = ma

Let N = 0, just touching

Summary of ConceptsSummary of Concepts Uniform Circular Motion

Speed is constant Direction is changing Acceleration toward center a = v2 / r Newton’s Second Law F = ma

50