Question

A fly wheel of mass $140\text{kg}$ and radius $3\text{m}$ is rotating at $240\text{rpm}$. The angular acceleration of flywheel if it comes to rest, after $7$ rotations is (Assume constant angular acceleration)

• A. $\frac{16}{7}\pi \frac{rad}{s^2}$
• B. $\frac{-16}{7}\pi \frac{rad}{s^2}$
• C. $\frac{8\pi }{7}\frac{rad}{s^2}$
• D. $\frac{-8\pi }{7}\frac{rad}{s^2}$

Answer 1

The correct option is B $\frac{-16}{7}\pi \frac{rad}{s^2}$

Given, Initial angular velocity $\left({\omega }_o\right)=2\pi \times \frac{240}{60}=8\pi \frac{rad}{s}$
final Angular velocity $\left({\omega }_f\right)=0\frac{rad}{s}$

Given that flywheel undergoes 7 rotations, so angular displacement $\theta =7\left(2\pi \right)=14\pi$

From Kinematics equation
${\omega }_f^2-{\omega }_o^2=2\alpha \theta$
$0-64{\pi }^2=2\alpha \left(14\pi \right)$
$\alpha =\frac{-16\pi }{7}\frac{rad}{s^2}$