Question
An object is rotating with uniform angular acceleration. If the rotation is started from rest state then the angular displacement after time will be proportional to what power of time?
✓
Answer
From the second equation of rotational motion
$\theta=\omega_0 t+\frac{1}{2} \alpha t^2$
where $\omega_0=\text { zero }$
$\therefore \quad \theta=0 \times t+\frac{1}{2} \alpha t^2$
$\theta=\frac{1}{2} \alpha t^2$
Hence, $\alpha$ is the uniform angular acceleration.
$\therefore \quad \theta \propto t^2$
$\theta=\omega_0 t+\frac{1}{2} \alpha t^2$
where $\omega_0=\text { zero }$
$\therefore \quad \theta=0 \times t+\frac{1}{2} \alpha t^2$
$\theta=\frac{1}{2} \alpha t^2$
Hence, $\alpha$ is the uniform angular acceleration.
$\therefore \quad \theta \propto t^2$
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