Question

A flywheel of mass $2$ kg and radius $20$ cm has an angular speed $50$ $rad{s}^{-1}$. When a clutch plate of mass $4$ kg, radius $10$ cm having an angular speed $200$ $rad{s}^{-1}$ is combined with it. Find the common speed of rotation.

• A. $125$ $rad{s}^{-1}$
• B. $150$ $rad{s}^{-1}$
• C. $175$ $rad{s}^{-1}$
• D. $100$ $rad{s}^{-1}$

Answer 1

The correct option is D $100$ $rad{s}^{-1}$

$\omega =\frac{I_1{\omega }_1+I_2{\omega }_2}{I_1+I_2}=\frac{2\left(.2{)}^2\right(50)+4(.1{)}^2\left(200\right)}{2(.2{)}^2+4(.1{)}^2}=\frac{12}{0.12}=100rad{s}^{-1}$