Question

A particle moves in a circular path of radius $20\text{cm}$ as shown. Find angular velocity of particle w.r.t an axis passing through centre of the circle and perpendicular to plane of the circle.

• A. $10\text{rad/s}$
• B. $15\text{rad/s}$
• C. $30\text{rad/s}$
• D. $40\text{rad/s}$

Answer 1

The correct option is B $15\text{rad/s}$

We know that relation between speed and angular velocity is,

${\omega }_{AC}=\frac{(v_{AC}{)}_{\perp }}{AC}$

Given $v_A=3m/s$,
So, $v_{AC}=v_A=3m/s$

As the radius is $20\text{cm}$, the distance of $AC$ will be $20\text{cm}=\frac{20}{100}\text{m}$

$\Rightarrow {\omega }_{AC}=\frac{3}{20\times \frac{1}{100}}=15\text{rad/s}$

Hence option B is the correct answer.