Answer to Question #249453 in Classical Mechanics for aisme

Question #249453

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.


1
Expert's answer
2021-10-10T18:10:57-0400

"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."


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