Circular Motion

Physics

Imagine a hammer (athletics variety) being spun in a horizontal circle

At a constant speed

Parts of a circle

R = the radius of the circle

The circumfrence is found by using the formula 2R or D (D=the diameter of the circle)

The area is found by using the formula R2

R

Examples of Circular motion Hard Drive CD Player DVD Record player Merry go round Sling-shot Bucket on a rope Orbiting planet Swinging Christmas tree lights

Circular Motion

Rotational Speed: Revolutions per second

Tangential Speed: Total distance per secondSame Rotational Speed

Different Tangential Speeds

Important facts:

An object traveling in a circle has linear, and rotational speed.

Linear speed is measured in m/s

Rotational speed is measured in cycles per second. (frequency)

Linear Speed

Important Facts:

Even if the object is moving at constant speed, the object is accelerating, because it is changing direction.

The direction that the objects changes to is always towards the center of the circular path.

Why does it accelerate Inward? In order for an object to accelerate their

must be a net force acting on the object (Newton’s second law)

The force must be pointing towards the center of the circle.

                     

The force to the left is holding the rock inward…

It is coming from the string.

Other Examples

The picture to the right is of a car traveling around a corner.

The centripetal force is coming from friction

The next picture is the moon traveling around the earth.

The force is coming form the gravity of the earth.

                               

Question:

What would be the force called on a loop the loop on a roller coaster?

Label the forces at the bottom sides, and top of the loop.

What is happen when your car make right turn? For an object to stay in circular motion,

there must be a force constantly pulling it towards the center of the circular motion.

How do we calculate the motion? Acceleration:

ac = v2

r Force

Fc = mv2

r

Symbols

v = tangential (linear) speed of the object

ac = centripetal acceleration

Fc = centripetal force

r = the radius m = mass T = period (time to complete one circle)

Which car is easier to turn? Big mass or small mass? Fast car or slow car? Centripetal force is required amount of

force pulling towards the center of the circle for the object to stay in circular motion.

Velocity

T

Dv

rD 2

T

rv

2

T = period time for 1 rotation

Also

Frequency rotations per sec

Tf /1

Centripetal vs. Centrifugal

The centripetal force is the force that causes an object to travel in a circle.

The centrifugal force is the inertia of the object that makes it want to continue in a straight line. There really is no such thing as centrifugal

force… it is only inertia.

Examples

A 150 g ball is tied to a string. If a student swings the ball so that it has a radius of .600 m, and a frequency of 2 rev/s, (a) what is the centripetal acceleration, and (b) what is the centripetal force?

Draw a diagram first to find the speed.

Examples

The earth revolves around the sun once a year. If the radius is 149.6 x 106 km, what is the acceleration that the earth encounters?