CIRCULAR MOTION

 

Angular velocity, w = angular displacement per unit time =

 

Relation between linear velocity and angular velocity

 

v= rw , where r is the radius of circular path

 

Centripetal acceleration acts along the radius & is directed towards the centre of circle. It is given by

a_c = rw² =

Angular acceleration () is the rate of change of angular velocity over time.

 =

Tangential acceleration (a) is the rate of change of linear velocity over time.

a =

Relation between tangential acceleration and angular acceleration

a = r

 

 

                                                            LAWS OF MOTION

 

 

Momentum (p) of a body is the product of its mass (m) and velocity (v)

 p = mv

 

Newton’s second law of motion gives the relation between force, mass and acceleration.

 

F = ma

 

Impulse = F x t = change in momentum

 

Centripetal Force = mv²/r

 

Atwood Machine: In simple Atwood machine, two masses are connected to the ends of an inextensible string passing over a pulley. If the pulley is frictionless,

 

 

Tension in the string is

T =

Acceleration of the masses is

a =

Banking of curved tracks: The optimum speed for making a vehicle negotiate the bend of radius ‘R’ without calling friction into play is

v = ,  is the angle of banking