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  4. The magnitude of displacement of a particle moving in a circle of radius a with constant angular speed ω varies with time t is

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

Motion in a Plane

Solution:

In time $t$ particle has rotated an angle $\theta= \omega t$. Displacement
image
$s =PQ=\sqrt{QR^{2}+PR^{2}}$
$s=\sqrt{\left(a\, \sin\, \omega t\right)^{2}+\left(a- a\,\cos\, \omega t\right)^{2}} $
$s=2a\, \sin \frac{\omega t}{2}$