Question

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

• 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