Question

Two flywheels A and B are mounted side by side with frictionless bearings on a common shaft. Their moments of inertia are $5kg{m}^2$ and $20kg{m}^2$ respectively. Wheel A is made to rotate at $10$ revolutions per second. Wheel B, initially stationary is now coupled to A with the help of a clutch. The rotational speed of the wheels will become:

• A. $2\sqrt{5}rps$
• B. $0.5rps$
• C. $2rps$
• D. $5rps$

Answer 1

Answer: (C)

$2rps$

When wheel B, initially stationary is coupled to A with the help of a clutch, both will have a common angular velocity and let that be $\omega$.

Since there is no external torque, angular momentum will be conserved. From conservation of angular momentum, $I\omega =I_1{\omega }_1+I_2{\omega }_2=5\times 10+20\times 0=50$

$\therefore (5+20)\times \omega =50$

$\therefore \omega =2rps$