Circular Motion Notes : Short Notes on radial vector,angular displacement & angular velocity

Circular Motion

Definition of Circular Motion:  

1.    Motion of a particle along the circumference of a circle is called circular motion.

2.    Examples: 

     I.         The motion of a cyclist along a circular path. 

   II.          Motion of the moon around the earth.

Definition of radius vector:

1. A vector drawn from the center of a circle to position of a particle on circumference of circle is     called as ‘radius vector’.

2. It is given by, 

 

     where,  δs = small linear distance

          δθ = small angular displacement 

3. It is directed radially outwards.

4. Unit: meter (m) in SI system and centimeter (cm) in CGS system.

5. Dimensions: [ M⁰ L¹ T⁰ ]

radius vector

    Definition of angular displacement:

1.    Angle traced by a radius vector in a given time, at the centre of the circular path is called as angular displacement.

2.    Consider a particle performing circular motion in anticlockwise sense. Let,

 A = initial position of particle at t = 0

 B = final position of particle after time t

 θ = angular displacement in time t 

 r = radius of the circle 

 s = length of arc AB

 Angulardisplacement is given by,  

3.    Unit: radian (rad)

4.  Direction of angular displacement is given by right hand thumb rule or right handed screw rule

angular displacement

Notes on angular velocity:

1.  Definition: Angular velocity of a particle performing circular motion is defined as the rate of   change of limiting angular displacement with respect to time 

2.  Instantaneous angular velocity is given by,

3.  Finite angular velocity is a vector quantity and it is given by,

4.  Direction: The direction of angular velocity is given by right hand rule and is in the direction of angular displacement.

5. Unit: rad s⁻¹

6.  Dimensions:  

angular velocity