Question

A stationary wheel starts rotating about its own axis with an angular acceleration of $5.5rad/s^2$. To acquire an angular velocity $420$ revolutions per minute, the number of rotations made by the wheel is:

• A. $14$
• B. $21$
• C. $28$
• D. $35$

Answer 1

Answer: (C)

$28$

Given, angular acceleration $\alpha =5.5rad/s^2$

angular velocity$=420rpm=420\times \frac{2\pi }{60}$
$=14\pi rad/s$

${\omega }_1^2-{\omega }_2^2=2\alpha \theta$

or, $(14\pi {)}^2=2\times 5.5\times \theta$

or, $\frac{98{\pi }^2}{5.5}=\theta$

$\therefore$ no of revolutions $=\frac{\theta }{2\pi }=\frac{49\pi }{5.5}=28$