I assume you mean there is non-slipping friction between the platform and wheel 2? Like a lossless rack and pinion.
Find out kinematic equations of motions for wheel 1 and wheel
2. Compare theirs translational and angular accelerations.
Two issues:
1. I don't like this equation:
Fs2 = Fl + Fr
It suggests that only part of Fs2 contributes to translational motion, but in fact all of it does. However I might be misunderstanding your meaning.
2. You seem to have neglected the angular acceleration of object 1. To balance angular momentums you have to sum all the angular momentums in the system, taken about the same axis.
Translational motion of wheel 1:
Fs1 = m * a1
Translational motion of wheel 2:
Fs2 = m * a2
Rotational motion of wheel 2 about its center:
Moment = I * angular acceleration:
Fs2 * R = I * alpha
Rotational motion of wheel 1 about the same point. +ve is clockwise:
Here I_1 means rotational inertia of object 1 about the center of object 2 for the type of motion it has, which includes no rotation of itself, so it's own 'I' must be ignored: I_1 = m * R^2
Moment = I_1 * angular acceleration:
Fs1 * R = I_1 * alpha_1
Fs1 * R = m * R^2 * alpha_1
What's alpha_1? Depends on the linear acceleration:
alpha_1 = a1 / R
Fs1 * R = m * R^2 * a1 / R
Fs1 = m * a1
This agrees with the linear motion equation, so no problem.
Qualitatively:
Translational:
Linear momentums easily cancel out.
Rotational:
If m is very high compared to I, then object 2 will spin up fast and get some angular momentum (high alpha, low I).
The objects will drift apart slowly because of their large masses. Object 1's angular momentum about the center of object 2 is also the same (low alpha, high I). I is high because it's proportional to the high m. Alpha is low because it's proportional to the low linear velocity.
So the two angular momentums can cancel out.
