Answer to Question #249453 in Classical Mechanics for aisme

Question

A flywheel of moment inertia 95 kgm^2 rotates about its axis with an angular velocity 60 rad/s. Coaxial with the flywheel is a gear-wheel of moment inertia 5.0 kgm^2, initially stationary. The two wheels are then joined together.

Calculate the angular velocity of both wheels together after they have been joined.

Answer 1

$E_1+E_2=E,$

$E_2=0,$

$E_1=\frac{I_1\omega_1^2}2,$

$E=\frac{(I_1+I_2)\omega_2^2}2,\implies$

$\omega_2=\omega_1\sqrt{\frac{I_1}{I_1+I_2}}=58.5~\frac{rad}s.$