Question

The magnitude of displacement of a particle moving in a circle of radius $a$ with constant angular speed $\omega$ varies with time $t$ is

• A. $2asin\omega t$
• B. $2asin\frac{\omega t}{2}$
• C. $2acos\omega t$
• D. $2acos\frac{\omega t}{2}$

Answer 1

Answer: (B)

In time $t$ particle has rotated an angle $\theta =\omega t$. Displacement



$s=PQ=\sqrt{Q{R}^2+P{R}^2}$

$s=\sqrt{{\left(a\sin \omega t\right)}^2+{\left(a-a\cos \omega t\right)}^2}$

$s=2a\sin \frac{\omega t}{2}$