Hi, first time on this forum. Thought the question and answers were interesting and felt like posting a reply. Basically, if all forces acting on the bike are kept constant, the bike's direction and speed and radius will not change (Newton's First law). If you change one of the forces acting on the bike - in this case applying throttle - the behaviour of the bike will be changed until it reaches a new equilibrium state - in this case in the form of a wider radius (Newton's Third Law). The reason is this:
Applying throttle increases the force exerted by the tyre on the road beneath it. This force is at a lean angle, but can be described as a function of a straight downward vertical force and a straight horizontal outward force. Accordng to Newton's Third Law, the road (Earth) exerts an opposite and equal force on the tyre, ie upward and inwards, effectively causing the tyre to be pushed in and under the bike, raising the bike and increasing the angle.
Applying throttle raises the bike, it's that simple. If you increase the speed of your bike in a corner and you don't widen your radius, it's because you lean in more or apply bar pressure, even if it's only slightly.
