circular motion2

Circular MotionCircular Motion

standard standard competencecompetence

Goal of learning

Materials

Class/Semester : x/IClass/Semester : x/I

By : Dra. PUDJIATIBy : Dra. PUDJIATIExercise SMA NEGERI 3 SEMARANGSMA NEGERI 3 SEMARANG

Standard Competence :Standard Competence :1.1 Apply the concepts and the 1.1 Apply the concepts and the basic principles of kinematics and basic principles of kinematics and dynamics.dynamics.Based Competence :Based Competence :2.1 Analyze physical quantity on 2.1 Analyze physical quantity on circular motion with constant circular motion with constant speed.speed.

Circular MotionCircular Motion

Goal of learningGoal of learning After learning this chapter, you are After learning this chapter, you are

expected to be ableexpected to be able IIdentify the dentify the physical physical quantities of quantities of

circular motion with circular motion with constant velocityconstant velocity Identify the formula of uniform Identify the formula of uniform circular circular

motion motion Identify the formula of wheels Identify the formula of wheels

connectionconnection Identify the formula of accelerated Identify the formula of accelerated

uniform uniform circular motion circular motion

The Quantities of Circular MotionThe Quantities of Circular Motion PeriodPeriod

FrequencyFrequency

Angular Angular distance or distance or Angular Angular displacemedisplacementnt θ = x/ Rθ = x/ R

WhereWhereTT - period (s) - period (s)n n - the sum of rotation- the sum of rotationf f  - frequency (Hertz) - frequency (Hertz)tt - rotating time (s) - rotating time (s)θ - θ - the angular displacement the angular displacement

or distanceor distance (rad)(rad) x - x - the linear displacement or the linear displacement or

distance (m)distance (m)R R - the radius of the path (m)- the radius of the path (m)

Polar Coordinates:Polar Coordinates: The arc length The arc length xx (distance along the circumference) is related to the angle in a simple way: (distance along the circumference) is related to the angle in a simple way:

x = Rx = R, , where where is the is the angular displacementangular displacement.. units of units of are called are called radiansradians..

For one complete revolution:For one complete revolution:22R = RR = Rcc

c c = 2= 2

has has periodperiod 22..

RR

vv

x

y

(x,y)x

1 revolution = 21 revolution = 2radiansradians

The Relationship of Angular Velocity The Relationship of Angular Velocity with Period and Frequencywith Period and Frequency

The Relationship of Angular Velocity with Linear Velocity

Where Where ωω - angular velocity (rad/s) - angular velocity (rad/s)vv - linear velocity (ms - linear velocity (ms-1-1) ) 

The Uniform Circular MotionThe Uniform Circular Motion Angular Distance or DisplecementAngular Distance or Displecement

Angular VelocityAngular Velocity

Angular AccelAngular Acceleerationration

0

t 0

0

000

tt

0)0( RRat

RmRvmFS

22

oTangential Acceleration

o Centripetal Acceleration

o Centripetal force

The Wheels Connection For two wheels that connected on center,

thus the direction of rotation same with the angular velocity.

or For two wheels that touch connected, thus

the direction two of them is adversative, and the angular velocity is samevv11 = v = v22   or or ωω11RR11 = ω = ω22RR22

For two wheels that connected with string or chain, thus the direction of rotation and the linear speed two of them is same

Accelerated Uniform Circular Motion

Angular Distance or Displecement

If , then then Angular Velocity

Angular Accelaration a =

WhereWhere aa - total acceleration (m/s - total acceleration (m/s22))

200 2

1 att

00 20 2

1 att

t 0

22ts aa

Example: Car rounding a bendExample: Car rounding a bend

Example: Car rounding a bendExample: Car rounding a bend

Example: Roller CoasterExample: Roller Coaster

Example: SatelliteExample: Satellite

Example: Solar System ?Example: Solar System ?

Non-examplesNon-examples

Most planetary orbits are not perfectly circular – Most planetary orbits are not perfectly circular – they are they are ellipticalelliptical..

However, sometimes we can However, sometimes we can approximateapproximate the the ellipse as a circle when we perform calculations.ellipse as a circle when we perform calculations.

Internal rotationInternal rotation is also a non-example of the is also a non-example of the circular motion that we are learning in this circular motion that we are learning in this lecture.lecture.

Why?Why?

Demo 1:Demo 1:horizontal circular motionhorizontal circular motion

Weight, Weight, mgmg

Normal, Normal, NN11

Normal, Normal, NN22

Demo 1:Demo 1:horizontal circular motionhorizontal circular motion

Normal, Normal, NN22

Normal, Normal, NN22

Normal, Normal, NN22

Demo 2: conical pendulumDemo 2: conical pendulum

Weight, Weight, mgmg

Tension, Tension, TTTTyy

TTxx

Centripetal forceCentripetal force In both examples, there is a In both examples, there is a net forcenet force acting on acting on

the object in a direction the object in a direction towards the centre of the towards the centre of the circlecircle..

This net force keeps the object in the circular This net force keeps the object in the circular path.path.

This net force is called the This net force is called the centripetal forcecentripetal force..

Linear velocityLinear velocity If the centripetal force is If the centripetal force is suddenly removedsuddenly removed, the , the

object will object will go off tangentiallygo off tangentially, i.e. no more , i.e. no more circular motion!circular motion!

This is because the This is because the instantaneous linear instantaneous linear velocityvelocity of the object is pointing in the tangential of the object is pointing in the tangential direction.direction.

Thus it is also called the Thus it is also called the tangential velocitytangential velocity..

Centripetal accelerationCentripetal acceleration& linear velocity& linear velocity

1. The centripetal force produces an acceleration towards the centre.

2. This acceleration is changing the direction of the linear velocity, so as to keep the object in the circle.

Back to the whiteboard…Back to the whiteboard…3.3. Quantitative UnderstandingQuantitative Understanding

Angular measure in radiansAngular measure in radians Angular velocityAngular velocity Centripetal acceleration & forceCentripetal acceleration & force

4.4. ExamplesExamples1)1) Conical pendulumConical pendulum2)2) Car going round a bendCar going round a bend3)3) Cyclist going round a cornerCyclist going round a corner4)4) AirplaneTension in the stringAirplaneTension in the string5)5) turning in a circular path in a horizontal planeturning in a circular path in a horizontal plane6)6) Vertical circular motion 1Vertical circular motion 17)7) Vertical circular motion 2Vertical circular motion 2

Jangan takut memanjat tinggi sebatang pohondan meraih dahannya.Di situlah buah-buah ranum bergantungan.-- Edward Linggar --

TTHANK YOU…HANK YOU…