Angular Speed

What is Angular Speed? When we witness the merry go round or a giant wheel rotating in a constant circular path, where motion is controlled from the center, one gets curious to understand the concept of motion in a circular track.
Also, there are movements like the motion of a car on a curved path, the motion of Moon about the Earth and motion of Earth around the Sun; one doesn’t see those motions focused at the center.

How are these motions being controlled? In answer to these questions arises the term centripetal force. This centripetal force develops because the body is continually speeded up, despite the fact that it is moving with constant speed. The centripetal force acts towards the epicenter of the circular motion and keeps the body in a circular path. Newton’s laws of motion is followed by this sort of motion.
Conferring to the first law of motion, the unbalanced force keeps the body moving in straight line track, therefore for the a body in a circular path, the presence of centripetal (unbalanced) force is a must.

Formula – angular speed

A scalar measure of rotation rate is known as Angular Speed (ω) .

In one complete rotation, angular distance traveled is 2π and time is time period (T) then,
angular speed = 2π/T


ω is equivalent to 2π f
where 1/T is equivalent to f (frequency)

Thus, the rotation rate is also articulated as an angular frequency.


Angular Speed and Linear Speed – Relation amidst them

Let the object be traveling in a round path of radius r and angular displacement be θ then we have, angle, θ = arc/radius
Angular Speed
We know that linear speed, V =S/t,
where S is linear displacement of arc, and
θ = S/r

Thus, linear speed V =(θ.r)/t
= r . (θ/t)

V = r ω

Hence, Angular speed,

ω = V/r
Where V is equivalent to the linear speed

This is the relation amongst angular speed, linear speed, and radius of the circular path.
From this relation, one can compute this speed.

Angular Speed of Earth

Our Earth takes about 365.25 days to finish one revolution around the Sun, now translate days into seconds,

T = 365.25 x 24 x 60 x 60 = 31557600 seconds
Angular speed = 2π/T

ω = 1.99 x 10−7 radians /seconds.

Unit of Angular Speed

Angular Speed is articulated as,

ω = V/r

linear speed is equivalent to V
the radius of circular path is equivalent to r

We get linear speed,

V = r . (θ/t)

∴ ω = (θ/t)
θ is articulated in radians.

So the elementary unit for this Speed is Radians per second or rps or rad/s.

Practise This Question

Four engines are working between the given temperatures ranges given below. For which temperature range the efficiency is maximum