Rotation with axle with unequally sized wheels https://youtu.be/hwgjMPaKMiA
In the above video, I have an assembly of two wheels of unequal radii connected via an axle. Now when we apply an external force anywhere on the axle, we see something different. Instead of going straight in the direction of the applied force, the whole assembly starts revolving in a circle.
There is another case when I connect only one end of the axle to a wheel and there is no wheel at the other end. Even then if I apply the force the wheel revolves in a circle instead of going straight in the direction of force.

Why exactly is this happening?plz help!
 A: 
When initially you exert a force $F_i$ to get things going, you're actually exerting a torque $T$ about the centre point of the circle:
$$T=F_i R,$$
with $R$ the radius of the circle.
According to Newtonian physics, this torque causes an angular acceleration $\dot{\omega}$ as follows:
$$F_i R=I\dot{\omega},$$
where $I$ is the Moment of Inertia of the wheels plus axis ensemble about an axis through and vertical to the centre point of the circle. This angular acceleration $\dot{\omega}$ starts the assembly rotating around the centre point of the circle.
Acting over a small period of time the actual angular speed $\omega$ is given by:
$$\omega=\dot{\omega} t.$$
The tangential speed $v$ (along the orbital trajectory is):
$$v=\omega R.$$
The radius of the circle can be seen to be $|AO|$ and can be derived as:
$$|AO|=\frac{R_L}{R_L-R_S}L,$$
with $R_L$ and $R_S$ the radii of the large and small wheels and $L$ the length of the connecting axis.
Once the force $F_i$ is withdrawn, the ensemble will continue rotating at constant angular speed $\omega$, on contdition friction provides enough centripetal force to keep the ensemble 'orbiting' around the centre point. The required centripetal force:
$$F_c=mR\omega^2,$$
is provided by the friction force $F_f$ which itself is given by:
$$F_f=\mu mg,$$
with $\mu$ the friction coefficient and $mg$ the weight of the assembly.
The scenario is the same when the smaller wheel is removed altogether: in that case the axis' end serves as an even smaller wheel.
