Round and Round

2-2-3 Circular Motion

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

t

dv

CIRCUMFERENCEC = 2πr = πdPERIOD (T)

Time for one revolution

T

rvc

2

Objects traveling in circular motion have constant speed and constantly CHANGING

velocity – changing in direction but not magnitude

Uniform Circular MotionHow do we define VELOCITY?

Velocity is TANGENT to the circle at all points

What ‘t’ are we talking about?What ‘d’ are we talking about?

• 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

Centripetal Force

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 “centrifugalforce” 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 wants

to go STRAIGHT

… but you can’t…The wall keeps pushing you back in toward

the center of the ride!

v

F

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

experienced from INSIDE a circular motion system – WHAT YOU FEEL

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

toward the center of a circular path – WHAT ACTUALLY HAPPENS

What is the sensation that you feel?

r

vac

2

Centripetal Acceleration• Centripetal force is a NET FORCE

• Causes ACCELERATION• In the SAME DIRECTION AS NET FORCE

• What is the centripetal acceleration of a toy ball on the end of a 1.44 meter long string if it is moving at 12 meters per second?

ac = v2/r

ac = (12 m/s)2/1.44 m

ac = 100 m/s2

Example #1

r

vac

2

Centripetal Force

m

Fa net maFnet cc maF

r

mvFc

2

• What is the centripetal force acting on a 2000 kilogram airplane if it turns with a radius of 1000 meters while moving at 300 meters per second?

ac = v2/r

ac = (300 m/s)2/1000 m

ac = 90 m/s2

Example #2

Fc = mac

Fc = (2000 kg)(90 m/s2)

Fc = 1.8 x 105 N

• Is it possible for a 1000 kilogram car to make a turn with a radius of 50 meters while moving at 15 meters per second with rubber tires on dry asphalt?

Fc = mv2/r

Fc = (1000 kg)(15 m/s)2/ 50 m

Fc = 4500 N

Example #3

Ff = μFN

Ff = (0.85)(9810 N)

Ff = 8339 N

Fc = 4500 N Ff = 8339 N

Yes, as long as Ff ≥ Fc

End of 2.2.3 - PRACTICE