Question

body travels along the circumference of a circle of radius 2 m with a linear velocity of 6 m/s . Then its angular velocity is *
(a) 6 rad /s
(b) 3 rad /s
(c) 2 rad / s
(d) 4 rad / s​

Answer 1

Given:

Body travels along the circumference of a circle of radius 2 m with a linear velocity of 6 m/s .

To find:

Angular velocity ?

Calculation:

• Angular velocity is an axial vector representing the rotational analogue of linear velocity.

• Let angular velocity be $\omega$.

$\rm \therefore \: \omega = \dfrac{v}{r}$

$\rm \implies \: \omega = \dfrac{6}{2}$

$\rm \implies \: \omega = 3 \: rad/s$

So, angular velocity is 3 rad/s

Answer 2

Given :-

• Radius = 2 metre .
• Linear Velocity = 6 m/s .

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To Find :-

• Angular Velocity = ?

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Solution :-

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∓ Here, we have to calculate the Angular Velocity of the body .

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★ Formula :- $\large\sf{\omega=\large{\frac{v}{ʀ}}}$

• $\omega$denotes to Angular Velocity .
• V denotes to Linear Velocity .
• R denotes to Radius of Cirlce .

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∓ Now, let's substitute -----

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$:\dashrightarrow\:\sf{ \omega = \frac{Linear\:Velocity}{Radius}} \\ \\ :\dashrightarrow\:\sf{ \omega = \cancel\frac{6}{2} } \\ \\ :\dashrightarrow\: \sf\red{ \omega = 3 \: rad\:/\:s}$

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Hence :-

• B option is correct [ 3 rad/s ] .

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