I was curious about what actually causes a bike to right itself when you brake while turning, found this on All Things (Safety Oriented) Motorcycle - Front Brake Stands Up Bike
If your bike's front-end is designed with a rake angle greater than zero (they all do), then use of the front brake while in a turn results in a significant tendency to straighten the bike up while widening that turn in the process. I will show why shortly.
The rear brake does the same thing, but with much diminished effect than use of only the front brake. That, because there is less weight transfer occurring with the use of the rear brake than with the front brake. Again, I will demonstrate that shortly.
Because of that rake angle, when you turn your handlebars, say 10 degrees to the left or right, the direction of travel is NOT changed by that same number of degrees - it is changed LESS than 10 degrees. Instead, some portion of the changed handlebar position is translated into shifting the contact patch forward relative to the body of the motorcycle. Furthermore, because your motorcycle is not a unicycle, when you change the steering angle it must travel some distance before that change of steering angle becomes the desired change of direction. The longer the wheelbase, and the greater the rake angle, the 'slower' your steering is.
Observe that as we turn the handlebars in these two diagrams a full 90 degrees that the center of the contact patch has moved forward from point 'B' to about 'C' (and that the front-end has lowered).
Had there been no rake angle (if the forks had been vertical) there would have been no forward displacement and the direction of change from a 10 degree turn would have been 10 degrees after the motorcycle had moved a sufficient distance for the body of the motorcycle to catch up with your intention. What happens when weight transfer is added to the picture is that the forks compress and as a result become more vertical - the rake angle gets smaller!. In other words, the steering becomes 'faster'
. Now a 10 degree turn of the handlebars results in a change of direction that is closer to 10 degrees than without any weight transfer.
Said differently, if you had already dialed in a 10 degree steering angle and then applied the brakes, you would have effectively turned your front tire slightly INTO the turn and that, as any fan of counter-steering knows, diminishes the lean angle and the track widens
So now we go on to front brake vs. rear brake effects.
Of course there is weight transfer when you use either. However, the amount of weight transfer is a function of the height of the CG as compared to the length of the wheelbase (and the deceleration rate, of course). Use of only the front brake maximizes weight transfer because as the front forks compress, as shown earlier, the rake angle diminishes and so, too, does the length of the wheelbase along with the height of the CG.
But by using only the rear brake you tend to straighten out the swing arm which lengthens the wheelbase and lowers the CG. Those things reduce the amount of weight transfer for any given rate of deceleration. As a result, the amount of weight transfer for any given rate of deceleration is less when using the rear brake than when using the front brake.
With less weight transfer, it follows that the front fork compression is also less and that, in turn, means that the tendency to go wide in a turn (and move toward vertical) is less.
Finally, let's look at that issue of 'steering speed' based on length of wheelbase.
By 'travel distance' I mean, of course, the front tire must move that distance to the left or right. Thus, the longer the wheelbase, the 'slower' the steering is.
-James R Davis