Skin Peeling From Scrotum

The bike's physics!

I took my best dish bike down a road Corsica, in a hairpin turn. I was not going particularly fast but my wheel was literally taken off in the curve, but I understand why. Only 25 years later, falling on a physics course by Walter Lewin of MIT I understand what happened and also lots of other s funny stuff about things turn. If English does not reject you, and you keep a painful memory of your high school physics course, jettez a look there. It is an extraordinary lesson in pedagogy to put all hands of teachers of physics.

Laws rotation
To understand how it works you just need a little reminder about the laws of motion of a rotating object on itself (but in the words of Arthur commentary, mathophobes can skip the next paragraph without problem). Do not worry it's easy

Simply replace:	by:
speed v	speed ω
mass m	the moment of inertia I = Σ (m i r i ²)
momentum p = mv	angular momentum L = I ω
force F	torque: C F = x r equal to the product of force by the distance to axis and perpendicular to both vectors

(vectors are in bold)

All the laws of motion are deduced from these analogies:

	In a move straight :	In rotation:
equation of motion:	force F = d p / dt	torque C = d L / dt
kinetic energy	E = ½ mv ²	E = ½ Iω ²
Labour	W = Fv	W = CW

When the angular momentum is conserved
If you do not follow, again, no big deal. The only thing that matters today is that in the absence of torque (ie force exerted on the axis of rotation), the angular momentum L = I ω is preserved, which is equivalent to the invariance of the momentum p = m v in the absence of force. It means nothing to you? This is the famous trick of the ice skater who turns on itself more and faster when it withdraws into her own arm and free foot. As it brings some of its mass toward the axis, its moment of inertia I = Σ (m i r ² i) decreases. Since the product I ω remains constant, the speed of rotation on itself ( ω) increases: that is why our beautiful skater speeds up when she cowers.

In a less gracious kind, when the volcano-which-does-anyone-know-it-pronounce name spits a lot of lava, it slightly changes the moment of inertia I of the Earth. And as I ω = constant, the speed of rotation of the Earth itself varies very slightly !

Bike Lesson No. 1: how to turn?
Let us return to my bike. I always hesitate to look me in the turns, lest it does drive out the wheel. This time, I were well kept because of gravel on the road, I simply turn the handlebars into the turn while remaining perfectly vertical. And then, boom ...
What happens when you try to rotate to the left a bicycle wheel spinning:


If the wheel was at rest, she would gently rotated in the direction where it grows. but when she turns it on the flip side! This gyroscopic effect is actually simple to understand: just remember that the axis of rotation of the wheel is still aligned with its angular momentum (remember L = I ω and ω represents the axis of rotation of the wheel). When you push on the axle of the wheel so it creates a pair angular momentum L two additional perpendicular to the thrust. The axis of rotation deviates so towards the new angular momentum.

Application to turn bike (or motorcycle) when driving and the handlebar is turned horizontally, it creates an angular momentum oriented vertically. (Remember the angular momentum is created perpendicular to the thrust on the handlebars). The axis of the wheel will therefore deviate towards the vertical, the wheel is not perpendicular to the road and flip the bike ...

So how do you turn the wheel while leaving the well perpendicular to the road? This is the ABC of the bike drive: just tilt the side where you want to rotate. Strangely to be very stable in a turn you must push down and certainly not turn the handlebars to the horizontal as I did.

Demonstration live when you are on a swivel stool:

The gyroscopes in action

are used to these strange properties to guide satellites in space and stabilize their position using small rotors attached to the satellite. Just change the orientation of the rotors slightly so that the satellite rotates on itself as in the previous experiment.

Now that the bike has no more secrets for you, you are ready to understand how a gyroscope can defy gravity. Take a bicycle wheel, rotate it on its axis and place its axis horizontally on a support:

The wheel not fall as he would if he were arrested, it turns around its horizontal support! A return to Newton in his grave? Not really: we are dealing exactly the same phenomenon as above, except that the gravity of the wheel (and opposite reaction of the support) replace the strength of the guy sitting on the stool swivel vertically when pressed on the axle of the wheel. If the speed of rotation of the wheel is great, the wheel turns to try to orient its axis of rotation to the angular momentum created by the weight of the wheel. Without ever succeeding course since the couple is still in the plane of the wheel. Just like the donkey who advance to catch the carrot hanging in front of his nose. More wheel weighs heavy more quickly it turns around the support.

Such "resistance" to gravity explains why a bike ride is stable vertically. And why a coin when you ride long lance on its edge. Gyroscopic phenomena also allow all sorts of pranks. Stash a wheel that rotates in baggage for instance and you get a bag very facetious:


Go to surpassing these adventures bicycle, a riddle: what goes down the more fast slope coasting:
- a large or small wheel?
- a solid wheel or a wheel "normal"?
- a heavy wheel or wheel light?

Curiously, the speed does not depend on the size of the wheels, or their mass ... Cons by a solid wheel moves faster than a hollow wheel because its moment of inertia from the center is smaller.

The acceleration is independent of the mass (M), radius R and is sixth times greater for a solid cylinder as a hollow cylinder

Demo image:

I guess that's why the wheels of the track bikes are solid discs. But in windy, beware of risks off!

Source:
Courses Walter Lewin (8.01) which are extracted from the MIT videos of this post.

similar Tickets:
Noether's theorem: Swiss Army knife of physics the origin of the laws of invariance