If the big grey box is one tonne, and the pivot, the small white circle has a diameter of 1 meter, how do I calculate the torque needed to turn it 360 degrees? Do i just use T=FD? but then I don't have the acceleration.
If there's no gravity any torque, no matter how small, would work. If there is gravity, then the applied torque must be sufficient to overcome whatever torque gravity might be applying as the box moves.
If there is gravity acting downwards the static torque required will be at a max when the thing has turned 90 degrees. You need to know the dimensions of the grey rectangle to calculate that.
Does it start from a stationary position? If so additional torque is required to accelerate it. How fast must it rotate? At what point in the rotation will the acceleration be at a maximum? Look up moment of inertia.