First of all, one must understand that a bicycle is actually an “inverted pendulum” (think of a pendulum, such as one in a clock, except upside-down). In other words, a bicycle will surely fall to one side if it is not balanced. We know this from everyday experience.

So, why is countersteering necessary? The concepts lie in basic mechanics. When riding a bike, turning the front wheel in one direction causes the bike to lean in the opposite direction due to a centripetal force. Therefore, the initial countersteering will cause the bike to lean into the direction of the desired turn. This lean is necessary because when executing the actual turn, there is a centripetal force that acts outward on the bike, and the force of gravity acting on the inward-leaning bike will cancel the outward centripetal force to keep the bike upright during the turn. If there is no inward lean during a turn, then the outward centripetal force will knock the bike over and cause it to fall down to the ground, resulting in a poor cycling experience for both the rider and the bicycle.

Despite being a necessity, countersteering isn’t something that is explicitly taught to a beginning bicyclist. It is something natural that is picked up when one attempts a turn on a bicycle for the first time. This makes countersteering an interesting and subtle phenomenon in bicycle dynamics.

Countersteering is important in bicycle dynamics.

Elevators come in handy when traveling many floors at a time.

Acceleration is a change in velocity over a period of time. Actually, this is specifically known as tangential acceleration (there are other forms of acceleration, namely that due to rotational motion, which may be discussed in a future post). The elevator’s motion can be broken down into three stages:

1. Start: the elevator accelerates from zero velocity (so you can step into the elevator safely) to its nominal travel speed.
2. Middle: the elevator travels at its nominal travel speed without speeding up nor slowing down.
3. End: the elevator decelerates (you can think of this as backwards acceleration) from its nominal travel speed to zero velocity (so you can step out of it and onto your destination floor safely).

The reason why you feel a force acting on your feet when the elevator starts up in the beginning and slows down at the end is because the elevator is accelerating during those stages. Newton’s second law states that force is directly proportional to acceleration. So, even if the elevator is moving very fast but at a constant speed, you will not feel an external force acting on you because there is no acceleration.

This same notion of not feeling anything different inside a moving vehicle (such as an elevator car) when there is no acceleration can also be applied to riding in a automobile on the road. When driving on the straight highway at a constant speed, you feel no external force acting on you and you sit comfortably. On the other hand, when you accelerate or decelerate your car, you feel a force pushing you back against the seat (during acceleration, or speeding up) or forward (during deceleration, or slowing down). Also, the force that you feel is directly proportional to the acceleration of the car, so if you speed up very quickly (which happens to not be very fuel-efficient) then you will feel a larger force.

Until next time, may your vehicular travels be smooth and comfortable without any jerky accelerations.

Impulse Equation

Impulse is another word for change in momentum, and is defined as force multiplied by time. Let’s consider two cases with the egg toss example:

1. You catch the egg with your arms and hands rigid (which means they do not move as the egg is caught). The egg’s motion comes to a complete stop when it hits your hands (and the insides of the egg are probably all over your hands as a result).
2. The egg is tossed at you at the same speed as in Case 1, and you catch the egg while moving your hands back along the motion of the egg, until the egg comes to a complete stop.

In both cases, the change in momentum of the egg is the same, because the egg’s initial speed and final speed (coming to a halt) are the same. What’s different between the two cases are the force applied to the egg, and the amount of time it takes to bring the egg’s motion to a stop.

In Case 1, the time that the egg took to come to a stop is extremely short: it was flying in the air at the speed at which it was thrown, and a split second later it came to a stop as it hit your rigid hands. Since the impulse of the egg remains constant, this means that the force acting on the egg during this split second is extremely large, which inevitably brings the egg to its doom and causes it to break.

On the other hand, in Case 2 the time in which the egg comes to a stop from it’s initial flying-in-the-air speed is much longer, because you were smart and moved your arms and hands with the egg as you caught it to bring it to a stop. By the same reasoning that the impulse remains constant, a long time implies that the force acting on the egg during that time is small. This significantly smaller force acting on the egg keeps it from breaking (if the force is small enough).

This principle of impulse to protect objects from breaking can be seen in many everyday devices. Some examples include airbags in automobiles, landing pads on the ground for gymnasts, and boxing gloves. The main idea behind all of these devices is that they deform when something hits them, which effectively increases the time required for a change in momentum, and therefore reduces the force acting on the incident object (in these cases, a person) onto the deforming safety device.