Originally Posted by
John C. Ratliff
Note in the example on this page of Newton's Cradle that the outside balls are traveling in an arc, not a straight line, because of the restraints of the two lines. The force in Newton's Cradle of gravity is subtractive, not additive in this case. The same would hold true for a bicyclist in the same type of collision above who holds onto the handlebars.
No, it would not hold true. The string is strong enough to provide the force necessary to allow the ball to swing in an arc, with that force being equal to mv^2/r (m = mass, v = linear velocity, r = radius of arc). The only way for a cyclist to achieve the same thing would be if his bike weighed enough to provide the same force that those strings are providing for the balls. With a 150 lbs. rider moving at 20mph and swinging in an arc of say 5 feet, the bike would need to weigh 173 lbs. to provide enough force to allow the rider to swing in an arc at that linear speed.
Conservation of linear momentum is the wrong concept to apply here because there is an outside force acting on the system. That force is whatever the rider has hit, which in the case of a pothole, the force applied is whatever force it takes to dislodge the rider from the bike (the pothole isn't going to give though the bike itself might). A cyclist traveling on a bike can be basically approximated by an object moving through space at a specific height. The bike is small enough and light enough that in a collision, the bike will do very little to alter the path of the cyclist. It may make them fall a little quicker or slightly slow the riders forward momentum as the bike gets crushed between the object being hit and the rider but that's it.