Question

A particle moves parallel to $x-$ axis with constant velocity $v$ as shown in the figure. The angular velocity of the particle about an axis passing through origin $O$ along Z-axis is

• A. remains constant
• B. continuously increases
• C. continuously decreases
• D. oscillates

Answer 1

The correct option is C continuously decreases

We know that, the angular velocity $\omega$ is equal to
$\Rightarrow \omega =\frac{v_{\perp }}{r}$, as $v_{\perp }=v\sin \theta$
$\Rightarrow \omega =\frac{v\sin \theta }{r}$
From $\Delta OAB$,
$h=r\sin \theta$

substituting the value of $r$ in $\omega =\frac{v\sin \theta }{r}$, we get

$\omega =\frac{v}{h}{\sin }^2\theta$
As particle moves more towards right $\theta \downarrow$, and so by the equation $\omega \downarrow$ ($\because \sin \theta \downarrow$ when $\theta \downarrow$)

Hence angular velocity decreases continuously.

Option C is the correct answer.