Uniform Circular Motion - Ms. Murphyuniform circular motion maintain a constant linear velocity, also known a tangential velocity, due to it’s inertia. Tangential velocity –the

Uniform Circular Motion

clip

A cycle is one unit of

motion that repeats.

A period (T) is the time it takes for one complete cycle, usually measured in seconds (s).

What is the period of each ball?

Blue ball revolves around the red dot in repeated cycles.

FrequencyThe frequency is the number of cyclesper unit of time. One common unit forfrequency () is the hertz (Hz).

1 Hz = cycle/second

Does ball A or B have the highest frequency?

Period and Frequency are inversely related. As period increase, frequency decreases.

Objects in uniform circular motion maintain a constant linear velocity, alsoknown a tangentialvelocity, due to it’s inertia.

Tangential velocity – the instantaneous

linear velocity of an object along the tangent to the object’s circular path.

Linear velocity equation:

For an object in uniform circular motion:

T = period of time for one revolution

vt

Objects in circular motion are accelerating.By definition, acceleration is a change invelocity. Since velocity is a vector quantity,acceleration may be a change in speed,direction or both.

Δt

Δva

5 m/s

5 m/s

5 m/s 8 m/s

Objects that move in circular

paths are accelerating, even

when they are traveling with

constant speed, because

they are constantly changing

direction.

Centripetal Acceleration

ac

vt

Tangential velocity

radius

Centripetal vs. Centrifugal

Centripetal forces-real forces that are directedtoward the center of anobject’s circular path.(friction, tension, gravity, etc.)

Centrifugal forces-

not truly forces because theyare attributable to inertia.

(no actual unbalance forcepushing out)

Remember F = ma?

Accelerations are the result of an unbalanced force acting on an object.

For objects in circular motion, the unbalanced force that produces circular motion is called centripetal force.

r

vmmaF

2

cc

Magnitude of velocity, tangential speed.

Mass of the object

Radius of the circular path

Centripetal acceleration

Net centripetal Force

Centripetal ForcesCentripetal forces are directed towardthe center of an object’s curved path.

Centripetal forces are

always

unbalanced

forces…because they result

in centripetal

accelerations…

accelerations that

change the direction

of an object’s path.

Fcentripetal

acentripetal

vtangential

You Can’t Always Trust What You Feel…

Frames of Reference

The passengers inertia is straight forward while the centripetal force is inward.

A Satellite

Fg

What is the centripetal force(s) that keeps a satellite in a circular path around the earth?

Car Rounding a Curve

mg

FN

Ff

What is the centripetal force(s) that keeps a car on the road while it’s turning?

In the Gravitron

mg

Ff

FN

What is the centripetal force (s) acting on a person in a Gravitron ride?

Example Problem:A test car (m= 800 kg) moves at a constant speed around a circular track.

If the car is 48.2 meters from the track’s center, and takes 20 seconds to

go around the track,

(a) What is the tangential speed?

(b) What is the centripetal acceleration?

(c) What is the centripetal force exerted on the car? mg

FN

Fs

Given: T = 20 s

r = 48.2 m

m = 800 kg

(b) ac= v2

r= (15.1 m/s)2

48.2 m

(c) Fc = mac = (800 kg)(4.7 m/s2) = 3760 N

= 4.7 m/s2

(a) vT = 2r/T = 2 (48.2m) / 20 = 15.1 m/s