Question

A particle is going parallel to x-axis with constant speed V at a distance a from the axis. Find its angular velocity about an axis passing the origin O, at the instant when radial vector of the particle makes an angle $\theta$ with the x-axis

• A. $\frac{V}{a}{\sin }^2\theta$
• B. $\frac{V}{a{\sin }^{}\theta }$
• C. $\frac{2V}{a}{\sin }^2\theta$
• D. $\frac{V{\sin }^2\theta }{2a}$

Answer 1

The correct option is B $\frac{V}{a{\sin }^{}\theta }$

Given,

Distance from origin O is $a$

Angle of radial vector is $\theta$

Agular velocity, $\omega =\frac{\text{tangential}\text{velocity}}{\text{perpedicular}\text{distance}}=\frac{V}{a\sin \theta }$

Hence angular velocity is $\frac{V}{a\sin \theta }$