Q.An object is executing uniform circular motion with an angular speed of $\dfrac{\pi}{24}$ rad s$^{-1}$. At $t = 0$ the object starts at an angle $\theta = 0$. What is the angular displacement of the particle after 4 s?

For a particle moving on a circle of radius $r$ about a centre O, the angle $\theta=\angle AOB$ swept out at the centre as the particle moves from position A to position B is its angular displacement, measured in radians, related to the arc length travelled by $\theta=s/r$ (equivalently $s=r\theta$). For a body rotating at a constant rate, the angular displacement after time $t$ is simply $\theta=\omega t$ (angular speed times time) when starting from $\theta=0$; more generally, under constant angular acceleration, $\theta=\omega_0t+\tfrac12\alpha t^2$ (the angular counterpar …