Circular Motion

(Chapter 9)

Describing Circular Motion

• Earth revolves around the Sun.

• Revolve—to spin around an external axis

• Earth rotates on its axis.

• Rotate—to spin around an internal axis

How quickly do you go around the circle?

Period (T)—time for one complete cycle of motion; SI unit is seconds (s)*

*But you can think of it as s/cycle!

frequency (f)—number of cycles of motion per time; SI unit is Hertz (Hz) where

s

cycleHz

11

What is the relationship between period and frequency?

fT

1

Do all people on a merry-go-round have the same speed?

• To find the speed of an object in uniform circular motion use:

T

rv

2

It depends.They all have the same angular speed ,because they all traverse the same number of degrees per second.People farther from the center have a greater linear speed because they travel more meters per second.

Velocity for objects in circular motion is always tangent to the

circle.

Does an object in uniform (constant speed) circular motion accelerate?

Yes, because the direction is changing!

What does an accelerometer tell us?

No motion Accelerating Accelerating

to the left to the rightNote that net force is always in the same direction as the

acceleration! (a = F/m!)

Force and acceleration in circular motion

• Force and acceleration are directed toward the center of the circle.

• The farther from the center, the greater the force and acceleration.

Centripetal Force

• Any force that makes an object go in a circle is a centripetal force.

• Always directed toward center of circle and perpendicular to velocity!

• To call a force a centripetal force is to categorize it based on its effect, not its cause. The cause may be gravity, friction, tension, etc…

Centripetal acceleration

• Always directed toward center of circle and perpendicular to velocity.

• Does not change speed of object, only direction!

Examples

What force keeps each object moving in a circle?(friction, gravity, horizontal component of tension)

Is the force directed toward the center of the circle?

Yes!

Equations for circular motion

Linear (tangential) Speed (v)

Centripetal acceleration (ac)

Centripetal force (Fc)

r

mvF

r

va

T

rv

c

c

2

2

2

REVIEW

1. A 800-kg race car drives around a circular track of radius 100 m in 30 seconds. Find:a. The periodb. The frequencyc. The tangential speedd. The centripetal acceleratione. The centripetal force.f. If the maximum force of friction between the tires and road is 10,000 N, how fast can the car drive before it slides off the track?

Centrifugal Force

• is the feeling of being thrown to the outside of a curve for objects in a rotating reference frame.

• It is a fictitious force because it is NOT an interaction between objects.

• It is actually the object’s inertia trying to make it go straight while its frame of reference rotates.

The ball goes straight while the board curves.

• Add an inward force on the ball and it curves, too!

Centripetal Acceleration and Force

2

2

c

c

va

r

mvF

r

Remember…

Both are directed toward the center of the circle!