Uniform Circular Motion

is the motion of an object in a circle with a

constant or uniform speed.

What is circular motion?

Anything that

rotates or

revolves around

a central axis is

in circular motion.

Rotation vs. Revolution

Rotation: an object turns about an

internal axis. “Spinning”

Revolution: an object turns about an

external axis, “Turning”

An axis is the straight line around which

rotation takes place.

Rotation vs. Revolution

Where is rotation?

Where is revolving?

As an object moves in a uniform circle

What happens to its speed?

What happens to its velocity?

What happens to its acceleration?

Identify the three controls on an

automobile which allow the car to be

accelerated.

conditions for uniform circular motion

A

V

Miniature golf: where will the golf ball go?

Over point A, B, or C?

A

B

C

B

What causes an object to have

Centripetal Acceleration?

Centripetal Force NOT centrifugal force

What’s the difference?

Centripetal = center seeking

Centrifugal = outward seeking

Without a net centripetal force, an object cannot

travel in circular motion. In fact, if the forces are

balanced, then an object in motion continues in

motion in a straight line at constant speed.

Without a centripetal

force, an object in

motion continues

along a straight-line

path.

With a centripetal

force, an object in

motion will be

accelerated and

change its

direction.

Courtesy http://www.physicsclassroom.com/mmedia/circmot/cf.cfm

frame of reference

Centripetal forces are those seen by an

observer in an inertial frame of reference.

Centrifugal forces are those felt by an

observer in an accelerating frame of

reference. As a car goes around a corner,

the passengers think they feel a force

towards the outside of the curve, in reality

this is due to inertia. Centrifugal force is a

misnomer!!!

What causes centripetal acceleration?

To have acceleration, there must be a net force

towards the center of the circle

What is the force for the following:

Earth circling the sun

Force of Gravity

Car turning a bend

Force of Friction

Xena warrior princess throwing a ball on a chain

Force of Tension on chain

conditions for uniform circular motionSpeed:

constant magnitude

Velocity:

constant magnitude, changing direction tangent

to circle

Velocity vector & acceleration vector:

perpendicular to each other.

Acceleration vector:

directed inwards

changes direction of the velocity vector not the

magnitude

Force vector:

directed inwards

Formulas

Calculating Period and Frequency

ond

srevolutionf

srevolution

ondsT

sec

sec

T = period or time

for one

revolution (sec)

f = frequency or

revolutions per

second (Hz or

sec-1)

Calculating speed

v = speed (m/s)

r = radius of circle

(m)

T = period or time

for one

revolution (sec)

f = frequency

T

rv

2

rfv 2

OR

Formulas

Calculating Centripetal Acceleration

using speed

ac = centripetal

acceleration (m/s2)

r = radius of circle (m)

v = speed (m/s)

av

rc

2

Formulas

Calculating centripetal force using

centripetal acceleration

Fc = centripetal force (N)

m = mass (kg)

ac = centripetal

acceleration (m/s2)

F mac c

r

mvFc

2

OR

Example

A little girl is swinging her 5 kg purse in

horizontal circles using the strap that

allows the purse to swing 20 cm from her

hand. The girl is able to get the purse to

make 10 revolutions in 8 seconds. What

was the speed of the purse? What is the

centripetal acceleration of the purse? How

much tension is in the purse string?

Example

Given:

m = r = T =

Example determine velocity

Given: m = 5 kg r = 20 cm = 0.2 m

T = (8sec / 10rev) = 0.8 sec/rev

T

rv

2

Example determine velocity

Given: m = 5 kg r = 20 cm = 0.2 m

T = (8sec / 10rev) = 0.8 sec/rev

sec/57.1

sec/8.0

)2.0(2

2

mv

rev

mv

T

rv

Example determine acceleration with

velocity of 1.57 m/s

Given: m = 5 kg r = 20 cm = 0.2 m

T = (8sec / 10rev) = 0.8 sec/rev

r

vac

2

Example determine acceleration with

velocity of 1.57 m/s

Given: m = 5 kg r = 20 cm = 0.2 m

T = (8sec / 10rev) = 0.8 sec/rev

2

2

2

/3.12

2.0

)/57.1(

sma

m

sma

r

va

c

c

c

Example determine FC with

acceleration of 12,3 m/s2

Given: m = 5 kg r = 20 cm = 0.2 m

T = (8sec / 10rev) = 0.8 sec/rev

maFc

Example determine FC with

acceleration of 12.3 m/s2

Given: m = 5 kg r = 20 cm = 0.2 m

T = (8sec / 10rev) = 0.8 sec/rev

NF

smkgF

maF

c

c

c

5.61

)/3.12)(5( 2

the average speed and the radius of the

circle are ________ proportional.

A twofold increase in radius corresponds

to a _______ increase in speed if period

remains the same

Concept questions:

An object moves in uniform horizontal circular motion. If the radius of the object triples, what happens to the speed of the object?

The speed will triple

How does doubling velocity affect the ac?

It increases four fold

How would calculating Fc change if the uniform circular motion was vertical instead of horizontal?