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

E1+E2=E,E_1+E_2=E,

E2=0,E_2=0,

E1=I1ω122,E_1=\frac{I_1\omega_1^2}2,

E=(I1+I2)ω222,    E=\frac{(I_1+I_2)\omega_2^2}2,\implies

ω2=ω1I1I1+I2=58.5 rads.\omega_2=\omega_1\sqrt{\frac{I_1}{I_1+I_2}}=58.5~\frac{rad}s.


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