An object moving in uniform circular motion is moving in a circle with a constant speed.

uniform:not changing in form or character;

remaining the same in all cases and at all times

uniform speed=constant speedspeed is how fast an object is moving

• An accelerating object is an object that has a change in velocity.

• Velocity is a vector—which has both magnitude and direction– a change in either the magnitude or the

direction (or both) means there is a change in velocity.

• For this reason, it can be said that an object moving in a circle at constant speed is indeed accelerating.

It is accelerating because the velocity is changing

directions.

An object moving in a circle experiences an acceleration.

This acceleration is directed TOWARD THE CENTER

of the circle.

For an object moving in a circle, there must be an inward force acting upon it in order to cause

its inward acceleration.

This force is called the

Centripetal Force.the word ‘centripetal’ means “center-seeking”

Newton's First Law of Motion (the Law of Inertia)

states that….

"... objects in motion tend to stay in motion with the same speed and the same direction unless acted upon by an unbalanced force."

Centripetal Force:a physical force pushing or pulling

the object towards the center of the circle.

The word "centripetal" is merely an adjective used to describe the

direction of the force. “center-seeking”

Examples of Centripetal Force

As a car makes a turn, the force of friction acting upon the turned wheels of the car provide the centripetal force

required for circular motion.

As the moon orbits the Earth, the force of gravity acting upon the

moon provides the centripetal force required for circular motion.

As a bucket of water is tied to a string and spun in a circle, the

force of tension acting upon the bucket provides the centripetal

force required for circular motion.

Newton’s Second Law states that….

• an object which experiences an acceleration must also be experiencing a net force.

• the direction of the net force always acts in the same direction as the acceleration.

The Centripetal Force causing an object to

move in a circle creates an acceleration that is

directed toward the center of the circle.

Equations to find Centripetal

Acceleration:

R

va

2

2

24

T

Ra

in otherwords

where:v is velocityR is radiusT is timeand pi is 3.14

Find the Centripetal Acceleration of a runner

running with a velocity of 8.8 m/s around a track with a radius of 25 m.

Find the Centripetal Acceleration of a car driving around an exit ramp with a velocity of

15 m/s. Assume the exit ramp has a radius of 30

m.

A dog sits 1.5 m from the center of a merry-to-round. The merry-

go-round is set in motion, and the dog’s speed is 1.5 m/s. what is

the dog’s centripetal acceleration?

A rope attaches a tire to an overhanging tree limb. A girl

swinging on the tire has a centripetal acceleration of 3.0 m/s2. If the length of the rope

is 2.1 m, what is the girl’s speed?

A race car moving along a circular track has a centripetal acceleration of 15.4 m/s2. If the car has a tangential speed of 30

m/s, what is the distance between the car and the center of

the track?