Introduction to the subject Motion

Circular Motion By- Prof. Dnyanesh

Vaidya

What does motion mean ?

Displacement of particle with respect to other particle is known as motion.

Types of Motion

Motion

Translational/Linear

Circular/Rotational

Oscillatory/Vibration

Circular motion Motion of a particle along the

circumference of a circle is called circular motion.

Position Vector or Radius Vector

A vector drawn from the centre of the circular path to the position of the particle performing circular motion at a instant, is called the position vector or radius vector

Angular Displacement Angular displacement θ of a

particle in a given time is defined as the angle traced by its radius vector in that time at the origin of frame of reference.

∴ angular displacement = ∠BOA = θ

arcBA

Butr

s

r

It is expressed in radian -------------- s

r

Angular Velocity

The rate at which the angular displacement takes place is called angular velocity (ω)

----------------------------

qvAverage angular velocityt

The instantaneous angular velocity can be obtained at limiting value of δt

----------------------------

t 0

dlim

t dt

It is measured in rad/sec.

U.C.M.“ Motion of a body along the circumference of a circle with

uniform linear speed or uniform

angular velocity.”

Angular Acceleration

The rate of change of angular velocity is called ‘angular acceleration (α)’

2 1

av t

i 2t 0

dw radlim It is measured in

t dt s

Thank You.