Two masses, having mass moments of inertia J1 and J2, are placed on rotating rigid shafts that are connected by gears. If the numbers of teeth on gears 1 and 2 are n1 and n2, respectively, find the equivalent mass moment of inertia corresponding to theta_1.
Kinetic energy of a rotating shaft = 1/2*J*theta_dot
J = 1/2*m*r^2
n1/n2 = theta_1/theta_2 ?????
The Attempt at a Solution
This is for my mechanical vibrations class for ME majors. I assume I need to relate theta_dot_1 to theta_dot_2 somehow. I am also not sure what to do with the number of teeth. It seems as though I may be able to do something with the gear ratio, but I don't know where to begin relating things. Please help!