# Wheel's torque and differential gearbox

I know that the differential gearbox is providing a torque to the wheels; as the relation in the figure indicates : Tw (wheel torque) = Td (differential torque) × (ηd×nd). Where nd:is the differential gear ratio and η:is the effeciency of the differential gearbox. Now this torque at wheels (Tw), which is provided by the differential , is also = Rw×Fx (torque from road friction ) . My question is : Won't the torque from (Fx) on the wheels accelerate (increase) the wheel's rotational speed(ωw) ? If this is the case;now ωw is increasing. And since (ωd=nd×ωw); then ωd(differential or driveshaft rotational speed) should also increase to maintain the gear ratio (nd) constant. So how would this differential/drive shaft rotational speed (ωd) increase to maintain this gear ratio (nd) constant ? • Why would the gear ratio be constant? the whole point of having gears is to match engine speed to road speed. Also will the torque be shared equally to both wheels? Jun 1 at 14:20
• So you are obviously saying that the gear ratio is not constant ; the gear ratio is teeth ratio of the input gear to the output gear . And of-course number of teeth will not change unless there was some magic happening in the gear-box Jun 1 at 14:28
• Based on this: So how would this differential/drive shaft rotational speed (ωd) increase to maintain this gear ratio (nd) constant Jun 1 at 14:34
• And there are gear drives with varying ratios… Jun 1 at 14:35
• @SolarMike Let's assume it the first gear ratio... Jun 1 at 14:38