Round and round…

Circular Motion

Circular Velocity

If this is true, why does ANYTHING move in a circle?

How do we define VELOCITY?

t

dv

What ‘d’ are we talking about?

CIRCUMFERENCEC = 2πr = πd

What ‘t’ are we talking about?

PERIOD (T)Time for one revolution

Velocity is TANGENT to the circle at all points

T

rvc

2

Objects traveling in circular motion have constant speed and constantly CHANGING velocity –

changing in direction but not magnitude

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

MisconceptionThe 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?

What is really happening?

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 keep pushing you back in toward

the center of the ride!

vcFc

What is it you feel?

• centrifugal (center fleeing) force– A ‘fictitious’ or ‘inertial’ force that is

experienced from INSIDE a circular motion system

• centripetal (center seeking) force– A true force that pushes or pulls an object

toward the center of a circular path

Centripetal Acceleration

r

vac

2

Unbalanced forces cause ACCELERATION

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

Centripetal force provides an unbalanced, net forcetoward the center of a circular path

Example #1

What is the centripetal accelerationof a toy ball swinging with a speed of

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

ac = v2 / r

ac = (12 m)2 / (1.44 m)ac = 100 m/s2

Calculating Fc

cc maF r

vac

2

r

mvFc

2

Newton’s 2nd Law?

F = ma

Example #3What is 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?

Fc = mv2 / r

Fc = (2000 kg) (300 m/s)2 / (1000 m)Fc = 180,000 N