Can a bicycle be tipped over by only applying rear brake?

[mrkevelev]

Let's say I'm riding a bike at constant speed. Also assume that the person riding is rigid, no moving of the persons body, constant center of gravity. Assuming that there is sufficient friction between the tires and road. If I apply the front brakes, I will likely tip over. If I apply the rear brakes, I will likely NOT tip over. If I only use the rear brakes, is it even possible to tip the bike over? What I think would happen is this:
I start decelerating. My center of gravity is above the pivot point on the front wheel, so I start to pitch forward. Because of the pitching moment, the friction of the rear tire on the road decreases. Since the grip has lessoned, the deceleration is less as well. Since the deceleration is less, there is nothing causing me to tip over. So I think there will be a constant balancing of forces, and therefore no tipping. I see this being the case even if the bike were quite taller, like you were riding on a tower (again, assuming no flexing). Is that the case? Not sure about skidding as well.

 

[lekh2003]

Ok, this is a question of torques. It is impossible that if you are moving forwards with significant speed, if you apply the rear brake that you would tip.

Let's examine the situation when you apply the front break. You are a cyclist with constant velocity and your front wheel automatically becomes a pivot point. In order for you to tip it over, there needs to be significant torque counterclockwise relative to the pivot point in order for the bicycle to tip. This torque is generated by your entire bike's and body's constant velocity. Mostly your upper body since that torque is directly in the direction you need to make the bike tip.

If you make the back wheel as the pivot, there is absolutely no way for the bike to tip. You could try some stuff like you said. Try and lean forward, but then again that is not pivoting around the rear wheel, but the front. See the attached image.

Is that the case?

Not too sure what you are saying here?

 

[jrmichler]

I start decelerating. My center of gravity is above the pivot point on the front wheel, so I start to pitch forward. Because of the pitching moment, the friction of the rear tire on the road decreases. Since the grip has lessoned, the deceleration is less as well. Since the deceleration is less, there is nothing causing me to tip over. So I think there will be a constant balancing of forces, and therefore no tipping.

Your description is correct, and easily verified by some experiments. For grins and giggles and because this is a physics forum, you could make a free body diagram, then work on the equations that prove it.

 

[A.T.]

If I only use the rear brakes, is it even possible to tip the bike over?

Theoretically yes. The rear brake force disappears quickly, but it does apply some angular momentum to the bike. Whether that angular momentum is enough to tip the bike, depends on how high the center of mass is compared to its horizontal distance to the front axle.

 

[lekh2003]

Theoretically yes. The rear brake force disappears quickly, but it does apply some angular momentum to the bike. Whether that angular momentum is enough to tip the bike, depends on how high the center of mass is compared to its horizontal distance to the front axle.

I think I understand what OP is saying. If the rear wheel is big enough and the center of mass is high enough, you could use the angular momentum to tip it over. I was only thinking in terms of linear momentum.

 

[A.T.]

I think I understand what OP is saying. If the rear wheel is big enough and the center of mass is high enough, you could use the angular momentum to tip it over. I was only thinking in terms of linear momentum.

Yes, but even when you neglect angular momentum of the wheels, it is theoretically possible to tip it over forward. Consider the torques around the center of mass of bike & rider.

The braking force applies an angular impulse to the bike & rider as a whole, which depends on the distance between center of mass and ground. After the back wheel lifts off, the frontal normal force transfers opposite angular momentum, which depends horizontal distance between center of mass and front wheel contact. You can theoretically adjust those two distances, such that the initial angular momentum is not completely canceled by the front wheel counter torque.