Question

A particle moves in a circular path of radius $40\text{cm}$ as shown. Find angular velocity of particle wrt an axis passing through centre of the circle and perpendicular to plane of the circle.

• A. $15\text{rad/s}$
• B. $12\text{rad/s}$
• C. $16\text{rad/s}$
• D. $14\text{rad/s}$

Answer 1

The correct option is B $12\text{rad/s}$

We know that relation between speed and angular velocity is,

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

Given $v_A=4.8\text{m/s}$,
So, $v_{AC}=v_A=4.8\text{m/s}$

As the radius is $40\text{cm}$, the distance of $AC$ will be $40\text{cm}=\frac{40}{100}\text{m}$

$\Rightarrow {\omega }_{AC}=\frac{4.8}{40\times \frac{1}{100}}=12\text{rad/s}$

Hence option B is the correct answer.