Q: A particle of mass m is revolving in a horizontal circle of radius r with a constant angular speed ω . The areal velocity of the particle is

(A) r^{2} ω

(B) r^{2} θ

(C) r^{2}ω/2

(D) rω^{2}/2

Solution :

Areal velocity = dA/dt ;

where A = area of the sector

=r^{2}θ/2

$\large \frac{dA}{dt} = \frac{d}{dt}(\frac{r^2 \theta}{2}) $

$\large = \frac{1}{2}r^2 \frac{d\theta}{dt} = \frac{r^2 \omega}{2}$