Circular Motion

Uniform circular motion (UCM)is the motion of an object in a perfect circle

with a constant (or uniform) speed.

• Another example of this would be you driving in a perfect circle at a constant speed.

• Are you accelerating? Constant or changing?• Do you feel pushed? Is there a force causing you

to accelerate?

What is the equation to find the speedof an object experiencing UCM?

T is the time for one cycle, aka, the period.

Since we are talking about a circular path this equation would change to:

• v = d/t• v = (circumference of circle)

(time to travel around the circle’s path)

v = 2 π r units: (m)T (s)

T = Period = the time for one complete cycle or the time for one complete revolution.Units: seconds/cycle or just seconds.

f = frequency = the amount of cycles (or revolutions) completed in a certain amount of time (usually one second).Units: cycles/second or Hertz (Hz)

Period and frequency are inverses of each other: T = 1/f

How would you describe the velocity in this situation where an object

is moving in a circle? • The velocity of an object

moving in a circle is constantly changing!

• We say the velocity vector is Tangent to the circular path of travel and call it the Tangential velocity.

Since the velocity is changing we can say an object moving in a circle is accelerating.• Since the velocity is changing at a constant

rate, we can say the magnitude of the acceleration is constant for an object experiencing Uniform Circular Motion.

• What is the direction of the acceleration? • Show accelerometer on turn table!• Acceleration is always directed inward

toward the center of the circular path!• Called Centripetal Acceleration! • (centripetal = center-seeking)

Remember from Newton’s First and Second Law, if there is a change in velocity there must be an outside force causing this acceleration.

• When you spin a bucket of water around your head, what direction do you apply a force on the bucket?

Remember from Newton’s Second Law:the direction of the net force is always the same as the direction of the acceleration!

The force causing an object to move in a circular path is an inward seeking force and is called the Centripetal Force.

Centripetal = center seeking

Do not confuse this with Centrifugal Force which is a description for the FEELING of

being pushed outward.(fake!) Centripetal – inward (center)

seeking, real.Centrifugal – outward fleeing,

fake.

The Math

This is it for the math

Force centripetal can be provided by…

• Tension Force (the tension in a string or rope)

• Friction Force (the friction between tires and road, or shoe and ground)

• Gravity Force (Earth experiences a force due to gravity while moving around the sun)

• Walls of a ride (amusement park ride)

http://www.youtube.com/watch?v=GauoEdyMZwY&feature=relatedhttp://www.youtube.com/watch?v=EnyKq7pO-c8&feature=related

https://www.youtube.com/watch?v=bpFK2VCRHUs

Go here to watch some videos… but have your earbuds plugged into your ears, please.