Round and round…

Circular Motion

Circular Speed & Velocity

• When objects move in a circular path, we will only consider those that have a constant speed.

• If speed is constant then is velocity constant?– NO, VELOCITY IS

ALWAYS CHANGING

v

vv

v

Circular Speed & Velocity

• Velocity changes because the direction changes as the objects goes around the circular path.

• VELOCITY IS ALWAYS TANGENTIAL TO THE CIRCULAR PATH

Centripetal Acceleration

r

vac

2

In order for velocity to change direction, the object must accelerate

Radius

Centripetal means: “Center Seeking”

The “Center-Seeking” Acceleration

ac

Example #1

Calculate the centripetal accelerationof a toy ball swinging with a speed of

12 meters per second on the end ofa 1.44 meter long string.

r

vac

2

m

a sm

c 44.1

)12( 2

2100s

mca

Example #2Calculate the velocity of a car that

experiences a centripetal acceleration

of 6 meters per second2 as it moves through a

turn with a radius of 5 meters.

r

vac

2

m

vs

m

56

2

2 smv 48.5

Centripetal Force

• Inertia causes objects to travel STRAIGHT

• Paths can be BENT by FORCES

• CENTRIPETAL FORCE bends an object’s path into a CIRCLE -- pulling toward the CENTER

vc , Fc , and ac constantlyCHANGE DIRECTION, but not MAGNITUDE

The “Center-Seeking” Force

Fc

Calculating Fc

cc maF r

vac

2

r

mvFc

2

Newton’s 2nd Law?

F = ma

Example #3Calculate the centripetal force on a

2000 kilogram airplane making a

turn with a radius of 1000 meters

if it is moving at 300 meters per second.

r

mvFC

2

m

kgF s

m

C 1000

)300)(2000( 2

NFC 000,180

Example #4

How far from the center of a merry-go-roundis a 500 kilogram horse that is travelingat 3 meters per second if it experiences

a force of 3000 newtons?

r

mvFC

2

r

kgN s

m 2)3)(500(3000 mr 5.1

THE GRAVITRONThe doors to the “Gravitron” close and it starts to spin.

You are pushed against the outside edge of the ride and

pinned there, You must be experiencing “centrifugal

force” throwing you outward from the ride! Right?

WRONG!

How is this possible?

As the Gravitron starts to spin,friction between your body and the ride

start you moving

Once you are moving, your body wantsto go STRAIGHT

… but you can’t…The WALLS push you back in toward

the center of the ride!

vcFc

SUMMARY• Compare circular SPEED & VELOCITY• How do objects change velocity in

circles?– Is it constant?– Equation?

• Which force causes circular motion?– Is it constant?– Equation?