- Motorcycles have only two wheels
- Motorcycles are rear-wheel drive
Cars are pulled by their front wheels (of course there are exceptions, but they are irrelevant for this discussion). The front wheels pull in their direction of travel. So, turn them to the right, and they pull in this new direction. The car is simply dragged along behind. The rear wheels will drag to the inside of the turn as they try to follow the front wheels. When the front wheels stop changing direction (the driver straightens out the steering), the car simply falls in line behind it. Nice and simple: turn the front wheels in the direction you want to go.
A motorcycle is driven by its rear wheel, and that wheel's orientation to the bike cannot be changed. What happens when you twist the front wheel of a motorcycle? First, you are impeding the forward motion of the bike slightly. The bike's momentum is going forward, but the front tire is now less free to spin in that direction. Second, you are lowering the front of the bike because of the front wheel's trail. These two effects combine to cause the bike to begin pivoting over it's front wheel (although the rear wheel won't actually leave the ground, hopefully). The third effect results from the front wheel's angular momentum. Since angular momentum is conserved, the change in the front wheel's orientation creates an angular force whose effect is to push the top of the steering column. Putting all of this together, we can now understand that twisting a motorcycle's steering column causes it to lean. Twist the steering column counterclockwise (push the right grip forward) and the bike will lean to the right. Twist clockwise and the bike leans to the left.
So now what happens? Well, with the bike leaning, its center of gravity is no longer directly over the bike's wheelbase. The effect of gravity causes the bike to lean even more. Now angular dynamics come in again. We have two spinning wheels being pivoted around their points of contact with the road so that their tops are being pulled downward. Angular momentum being conserved, each wheel experiences a force that pivots them around their vertical axis. Leaning to the right twists each wheel clockwise. The twist of the front tire can be felt as it pushes against your right hand. The twist of the rear tire is imparted to the bike's frame, causing the frame's orientation to twist clockwise (turn to the right).
So, push right to lean right, and push left to lean left. The lean initiates the turn. Hmm, how do we get out of this turn? Well, if we push back against the grip, we go through all of these effects again, making the turn more extreme. If we give in to the pressure, the front tire's orientation will turn even more (relative to the bike) setting up all of the opposite turn dynamics. The bike's momentum will carry its center of mass toward the outside of the turn, straightening up the bike.
That's the theory, anyway. It's time for an experiment. Get on your bike, ride in a straight line at a low but stable speed, and then twist the steering column by pressing and releasing one of the grips. Then try the other side. What happens? Pressing on the right grip doesn't turn the bike to the right, but instead leans the bike to the right. And a bike that is leaning will turn. So, countersteering doesn't so much turn the bike as it puts the bike in a position which will cause it to turn.