Question

The rotating rod starts from rest and acquires a rotational speed $\omega =600$ rev/min in $2$ seconds with constant angular acceleration. The time t after starting before the acceleration vector of end P makes an angle ${45}^o$ with the rod is?

Answer 1

Initial angular velocity $w_i=0$

Final angular velocity $w_f=600rev/min=600\times \frac{2\pi }{60}=20\pi rad/s$

Time $t=2s$

Using $w_f=w_i+\alpha t$

Or $20\pi =0+\alpha \times 2$

$⟹\alpha =10\pi rad/s$

Now, angle by which rod is rotated $\theta =\frac{\pi }{4}$

Using $\theta =w_{i}t+\frac{1}{2}\alpha t^2$

Or $\frac{\pi }{4}=0+\frac{1}{2}\left(20\pi \right)t^2$

$⟹t=\frac{1}{2\sqrt{10}}s$