Lucy W wrote:
If the argument ‘rotational momentum reaction’ is to be followed it’s like this. The reaction to the braking of the front wheel generates a reaction force proportional to the mass of the wheel, that rotates the car tail over bonnet about the centre of gravity. The braking on the rear wheel does the opposite and because the masses of the wheels are the same each force cancels one another out. Now surely you don’t need to be an Einstein to work understand that?
I understand what you are getting at now. You are assuming the rotation of the front and rear wheels balance out round the CoG.
This is not the case.
The rotational force, i.e torque, applied to the CoG is dependant on the distance at which the force is applied to the CoG.
This means the torque applied by the mass of the wheel further from the CoG is greater than that of the mass of the wheel closer to the CoG.
Imagine that instead of a wheel you have a bar running through the hub with a mass on either end, also that the CoG lies on a line between the hubs and equally distant. If you stop the bars when are in line with the axis between the hubs the masses furthest from the CoG will apply a torque greater than the masses closest to the CoG therefore there will be a net force trying to rotate the 'vehicle' around the CoG.
But wheels are not masses on the ends of rods are they? Well yes they are as far as the physics goes, just hold that thought for a moment.
Lets stop the wheels with the rods at say 45 degrees.
You now draw a line between the centre of each mass and the CoG, the force applied by each mass has a vector perpendicular to the rod they are connected to. This can be resolved into two components, one perpendicular to the line through the mass and CoG and one parallel with it. The perpendicular force is what causes the rotational torque around the CoG.
Now draw lines through the CoG and tangential to the circle described by the spinning 'wheels', the points at which these lines touch the 'wheels' are where the force applied to the CoG by the wheel changes direction. You will notice that the arc the masses describe while capable of applying a torque in one direction is greater greater than the other direction, further more as this arc's path occurs at a greater distance from the CoG the torque applied is also greater for any position along its length.
So, weights on bars are not wheels are they? Again, yes they are.
Lets add another bar and masses to each hub at right angles to the first, it is pretty easy to see that for any given position of the 'wheel' the resultant torque is always going to be in one direction. Add two more bars and masses to each hub, evenly spaced, in fact keep doubling the bars and masses and eventually the masses touch and we have a spoked wheel.
The torque applied about the CoG will in general be opposite to the direction of acceleration of the wheels, do not forget deceleration is just acceleration with a negative sign.
If the CoG is not equally spaced between the hubs or in line with the hubs the effect will still occur. Without doing the maths I cannot be certain, but in line at equal spacing is probably where you get the maximum torque.