** **__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} = rw^{2} = _{}

**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** = mv^{2}/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