Question

How much revolution does the engine make during the time when a motor wheel with angular speed is increased from $ 720\,rpm $ to $ 2820\,rpm $ in $ 1,4\,s $ ?

• A. $ 354 $
• B. $ 490 $
• C. $ 413 $
• D. $ 620 $

Answer 1

Answer: (C)

$\omega_{0}=2 \pi \times \frac{270}{60}$
$=24\, \pi rad / s \omega=2 \pi \times \frac{2820}{60}$
$=94\, \pi rad / s$
We know that, $\omega=\omega_{0}+\alpha t$
$94 \pi=24 \pi+\alpha(14)$
$\alpha=\frac{70 \pi}{14}=5 \pi rad / s ^{2}$
$\Rightarrow $ From $\theta=\omega_{0} t+\frac{1}{2} \alpha t^{2}$
$=24 \pi \times 14+\frac{1}{2} \times(5 \pi) \times(14)^{2}$
$=336 \pi+490 \pi=826 \pi$
$\Rightarrow $ The number of revolutions $=\frac{826 \pi}{2 \pi}$
$=413$ revolutions