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CIRCULAR MOTION

- Motion of a body in a curved path

TYPES:

Uniform Circular Motion, UCM motion with

constant speed

Ex. A car rounding an oval at 30 KPH

Non-Uniform circular Motion, NUCM a roller

coaster car that slows down and speeds up as it

moves around a vertical loop.

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V

VS

r

Conversion:

1 rev = 360 = 2 radc

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Concept in Uniform Circular Motion

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5.3Centr ipetal Force

aF

m

m

Fa

Recall Newtons Second Law

When a net external force acts on an objectof mass m, the acceleration that results is

directly proportional to the net force and has

a magnitude that is inversely proportional tothe mass. The direction of the acceleration is

the same as the direction of the net force.

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Definition of Terms

rectilinear

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5.3Centr ipetal Force

Thus, in uniform circular motion there must be a net

force to produce the centripetal acceleration.

The centripetal force is the name given to the net force

required to keep an object moving on a circular path.

The direction of the centripetal force always points toward

the center of the circle and continually changes directionas the object moves.

rvmmaF cc

2

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Uni form Circular Mot ion

Period, T- time it takes for the object to

travel once around the circle. (sec)

Frequency, fno. of cycles/revolutions per unit time

(rev/sec, cycles/sec, hertz)

r

= 1/

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Summary

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Sample Problems

A Tire-Balancing Machine

1. The wheel of a car has a radius of 0.29m and it being rotatedat 830 revolutions per minute on a tire-balancing machine.

Determine the speed at which the outer edge of the wheel is

moving.

The Effect of Speed on Centripetal Force

2. The model airplane has a mass of 0.90 kg and moves at

constant speed on a circle that is parallel to the ground.

The path of the airplane and the guideline lie in the same

horizontal plane because the weight of the plane is balancedby the lift generated by its wings. Find the tension in the 17 m

guideline for a speed of 19 m/s.

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Sample Problems

3.

5.

4.

If the oval will be flat, what must be the what must be the coefficient of

friction between the tires and the road so the cyclist can turn safely?

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Sample Problems

7.

6.

vertical.

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A Body Moving In Circular Path on a

Flat Horizontal Surface

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Forces Acting on a Body When Rotated forming a

Vertical Circle (when along the horizontal)

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Vert ical Circular Mo tion

r

vmmgF

N

2

1

1

r

vmmgF

N

2

3

3

r

vmFN

2

2

2

r

vmFN

2

4

4

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VertiVertical Circle A Rotating Ferris Wheel

B k d C

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Banked Curves

On an unbanked curve, the static frictional force

provides the centripetal force.

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Car Rounding a Flat Curve at Constant Speed

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Banked Curves ( Neglect ing Fr ict ion)

r

vmnFc

2

sin

mgn cosrg

v2

tan

n

n cos

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Conical Pendulum