Question

If a car moves with a uniform speed of 2
m/sec in a circle of radius 4m its angular
speed is
A. 4 rad/sec
B. 5 rad/sec
C. 2.5 rad/sec
D. 6 rad/sec​

Answer 1

Given :

• Uniform speed = 2 m/s.

• Radius = 4 m.

To find :

Angular speed of the car.

Solution :

We know the relationship between linear speed and Angular speed i.e,

$\boxed{\bf{v = \omega R}}$

Where :

• v = Linear speed
• ω = Angular speed
• R = Radius

From the above equation , we get :

$:\implies \bf{v = \omega R}$

$:\implies \bf{\dfrac{v}{\omega} = R}$

$:\implies \bf{\dfrac{1}{\omega} = \dfrac{R}{v}}$

$:\implies \bf{\omega = \dfrac{v}{R}}$

$\boxed{\therefore \bf{\omega = \dfrac{v}{R}}}$

Hence the formula for Angular speed we get as , $\bf{\omega = \dfrac{v}{R}}$

Now by using the formula for Angular speed and substituting the values in it, we get :

$:\implies \bf{\omega = \dfrac{v}{R}}$

$:\implies \bf{\omega = \dfrac{2}{4}}$

$:\implies \bf{\omega = \dfrac{\not{2}}{\not{4}}}$

$:\implies \bf{\omega = \dfrac{1}{2}}$

$:\implies \bf{\omega = 0.5}$

$\boxed{\therefore \bf{\omega = 0.5\:rad\:s^{-1}}}$

Hence the angular speed of the car is 0.5 rad/s.