CIRCULAR MOTION

CONTENTS

• CIRCULAR MOTION• ANGULAR DISPLACEMENT• ANGULAR SPEED• ANGULAR VELOCITY• CENTRIPETAL FORCES &

ACCELERATION

CIRCULAR MOTION • If an object/ body is moving along a circular

path it is said to be in circular motion.• Uniform circular motion : If the object move

with uniform speed along the circular path, it is said to have uniform circular motion.

• http://www.animations.physics.unsw.edu.au/mechanics/chapter3_circularmotion.html#3.1

Angular displacement• The angle through which the radius

vector representing the position of a particle rotates is called angular displacement

• The change in position of the particle in a circular path with respect to its centre is called angular displacement.

• The angular displacement of a body with respect to a reference line is denoted as θ.

Angular Displacement Units

• The angular displacement can be measured in degree.

• But the S.I. Unit for angular displacement is Radians.

• One radian is defined as the angle subtended at the centre of a circle by an arc which is equal to length of the arc divided by the radius of the circle.

Conversion between degree and radians

• When an object makes through a complete circle,

• angular displacement in the entire circle is 3600 = 2π radians

• 1 0 = 2π/ 180• 1 radian = 180 / 2π degrees

Question to check how far you understood

• By how many degrees does the angular displacement of the hour hand of a clock change each hour ?

Speed steady , but velocity ?• An object moving in uniform circular motion is

moving in a circle with a uniform or constant speed.

• Is it accelerating ?• Yes, because, it is changing the velocity.• Since velocity is a vector which has both

magnitude and direction, a change in either the magnitude or the direction constitutes a change in the velocity.

Angular velocity

• Angular velocity, also called rotational velocity, is a quantitative expression of the amount of rotation that a spinning object undergoes per unit time.

Vector – angular velocity

Centripetal acceleration

• An object moving in a circle is experiencing acceleration. Even if moving around the perimeter of the circle with a constant speed, there is still a change in velocity and subsequently an acceleration.

This acceleration is directed TOWARDS THE CENTER of the circle.

‘ω’ represents the angular velocity and ‘α’ represents the angular acceleration.

Centripetal force

• According to Newton’s second law of motion, every object which has an acceleration will experience a net force in the direction of acceleration.

Centripetal force

http://w3.shorecrest.org/~Lisa_Peck/Physics/syllabus/mechanics/circularmotion/Images/wi1.gif

So for an object moving in a circle, there must be an inward force acting upon it in order to cause its inward acceleration which is called centripetal force.The word "centripetal" means CENTER-SEEKING. For objects moving in circular motion, there is a net force acting towards the center which causes the object to seek the center.

Centripetal force

http://www.regentsprep.org/regents/physics/phys06/bcentrif/default.htm

http://phet.colorado.edu/en/simulation/legacy/gravity-and-orbits

Questions.

End of the chapter questions.