A current I1 carrying wire AB is placed near another long wire CD carrying current I2. If wire AB is free to move, it will have:

The magnetic field around the wire CD at a distance r from it = μ₀I₂/2πr
Thus the magnitude of magnetic field decreases along the wire AB due to wire CD.
On each small element of wire AB, force = I₁Bdr
Thus the force at each point is always in the upward direction but decreases in magnitude as we go from the nearer end to wire CD to the farther end.
Thus the translation is due to all forces acting in the upward direction and rotation is due to all forces being different in magnitudes.