Question

The rotating rod starts from rest and acquires a rotational speed $\omega =600$ rev/min in $2$ seconds with constant angular acceleration. The magnitude of acceleration for time t is?

Answer 1

Angular acceleration $\alpha =10\pi rad/s$

Angular velocity at time $t$, $w_f=w_i+\alpha t$

Or $w_f=0+10\pi \times t$ $⟹w_f=10\pi t$

So, centripetal acceleration at time $t$, $a_c=r{w}_f^2=100{\pi }^2{t}^2$

Tangential acceleration $a_t=r\alpha =1\times 10\pi =10\pi$

Thus magnitude of acceleration $a_{net}=\sqrt{a_t^2+a_c^2}=\sqrt{100{\pi }^2+10000{\pi }^4{t}^4}$