Question

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. r²ω
• B. r²θ
• C. $\frac{r^{2}}{2}\omega$
• D. $\frac{r\omega^{2}}{2}$

Answer 1

Answer: (C)

$\frac{r^{2}}{2}\omega$

Answer 2

Areal velocity = $\frac{dA}{dt}$ where A = area of the sector

= $\frac{r^{2}\theta}{2}$

∴ $\frac{dA}{dt}$ = $\frac{d}{dt}\left( \frac{r^{2}\theta}{2} \right)$ = $\frac{r^{2}}{2}\frac{d\theta}{dt}$ = $\frac{r^{2}}{2}\omega$.