CENTRAL CENTRAL ACCELERATIONACCELERATION

&&CENTRAL FORCECENTRAL FORCE

-- Acceleration of a body Acceleration of a body moving in moving in Uniform Circular Motion..

CENTRAL CENTRAL ACCELERATIONACCELERATION

Uniform Circular Motion

- Is the motion of an object - Is the motion of an object with uniform speed following a with uniform speed following a circular path.circular path.

CENTRAL ACCELERATIONCENTRAL ACCELERATIONFormula:Formula:

aacc = V = V22/R/RWhereWhere

aac c = central acceleration on the object= central acceleration on the object

V V = uniform circular speed= uniform circular speed

R = radius of the circleR = radius of the circle

Example ProblemExample Problem

An object is tied to a string An object is tied to a string

then whirled with a constant then whirled with a constant

speed in a horizontal circle with a speed in a horizontal circle with a

radius of radius of 1.2 meters1.2 meters. It takes . It takes 1.4 1.4

secondsseconds for the object to make for the object to make

one complete revolution.one complete revolution.

Find:Find:

a. a. VV ( speed of the object ) ( speed of the object )

b. b. aacc ( central acceleration on the ( central acceleration on the

object )object )

Given: Given:

R = 1.2 mR = 1.2 m t =1.4 st =1.4 s

Solution:Solution:

a. V = 2a. V = 2ллR / tR / t

V = 2(3.14)(1.2 m)/ 1.4 sV = 2(3.14)(1.2 m)/ 1.4 s

V = 5.38 m/sV = 5.38 m/s

b. ab. acc = V = V22 / R / R

aacc = (58.38) = (58.38) 22 / 1.2 m / 1.2 m

aacc = 24.12 m/s = 24.12 m/s22

C E N T R A L

F O R C E

- A central force is a force with a - A central force is a force with a

direction and magnitude that only direction and magnitude that only

depend on an object's center and the depend on an object's center and the

distance from its center to another distance from its center to another

point. point.

Centripetal ForceCentripetal Force

- - latin words words centrumcentrum ("center")("center") and and

peterepetere ("tend towards", "aim at"),("tend towards", "aim at"),

signifying that the force is directed inward signifying that the force is directed inward

toward the center of toward the center of curvaturecurvature of the path. of the path.

Centripetal ForceCentripetal Force

- - Isaac NewtonIsaac Newton's description was: 's description was:

"A centripetal force is that by which "A centripetal force is that by which

bodies are drawn or impelled, or in bodies are drawn or impelled, or in

any way tend, towards a point as to a any way tend, towards a point as to a

center."center."

- means - means “center seeking” “center seeking”

Formula: Formula:

FFc c = ma= macc

WhereWhere

FFc c = Centripetal Force= Centripetal Force

Centrifugal ForceCentrifugal Force

- opposite of - opposite of Centripetal Centripetal

Force.Force.

- - tends to keep the revolving tends to keep the revolving

body away from the center.body away from the center.

1.1. Formula of Central Formula of Central Acceleration.Acceleration.

2.2. What is the meaning of the What is the meaning of the Latin word Latin word “centrum”“centrum” ??

3.3. What force that tends to What force that tends to keep the revolving body keep the revolving body away from the center ?away from the center ?

4.4. What force that tends What force that tends towards the center?towards the center?

Give the meaning of the Give the meaning of the ff. symbols:ff. symbols:

5. V 5. V

6. F6. FC C

7. a7. acc

8 -10. Problem Solving8 -10. Problem Solving

A ball is tied to a string then whirled with a A ball is tied to a string then whirled with a

constant speed in a horizontal circle with a constant speed in a horizontal circle with a

radius of 25 meters. It takes 2 seconds for radius of 25 meters. It takes 2 seconds for

the ball to make one complete revolution.the ball to make one complete revolution.

Find: a. speed of the objectFind: a. speed of the object

b. central acceleration on the b. central acceleration on the

objectobject