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70

In comparing wheels of today to those in history, there are traditionally more spokes now. However, that's because wheels in the past (even large wagon wheels in not-so-ancient times) used relatively thick wooden spokes that behaved like a column and dealt with the load of the wheel with compression. However, modern spokes are very thin. Far too thin to ...


60

The astronaut can change his or her orientation in the same way that a cat does so whilst falling through the air. After the transformation, the astronaut is still and angular momentum is conserved. There is a rather beautiful way of understanding this rotation as an anholonomy i.e. a nontrivial transformation wrought by the parallel transport of the cat's ...


53

No, a car cannot steer on a frictionless surface. This has little to do with gyroscopic action and more to do with conservation of momentum: to turn, even when conserving its speed, the car needs to accelerate at right angles to its motion, which changes the total momentum of the motion. This change in momentum requires a force which, in normal roads, is ...


52

Your intuition about spinning fluids is wrong for a couple reasons. Angular momentum is conserved so an isolated system of any shape will keep on spinning unless it has a way to transfer that momentum elsewhere. If you spun in egg levitating in a vacuum it would spin forever. The more bumps, flaws, or non-spherical features your container has the faster ...


47

If the wheels had spun fast enough for a gyroscopic effect to become noticeable, the only result on a frictionless surface (which would be the same without a surface at all) is that when you turn the wheels, the rest of the car would rotate instead of just the front wheels :) You need some reaction force to alter the trajectory, like a sail or surface ...


31

For those that are cat-challenged, here's an alternative explanation and demonstration you can try at home! This demonstration was taught to me by my math lecturer. All you will need is: A swivel chair and a heavy object (e.g. a big textbook) Stand on the seat of the chair (watch your balance now) holding the heavy object. Extend your arms forward ...


26

Yes you can It is actually possible with a real car, but you would have to be very patient to steer a little bit. Suppose you have built a car with power on the big front wheels to induce a gyroscopic effect. If you rotate the wheels, the direction in which the center of mass is going will not change directly, but the angle in which the rest of the body ...


24

In start-up and hover each blade produces more or less constant sound. But the sound is attenuated by distance and may not be the same in all directions. Therefore you hear it differently depending on the blade's position relative to you. So as the blades rotate, the sound you hear pulsates because the blades alternately get to positions where you hear them ...


22

The Wikipedia article you linked states: Atomic clocks show that a modern day is longer by about 1.7 milliseconds than a century ago If we take this change of 1.7 ms/century and multiply by 2.5 million centuries (250 million years) then we get a change of 4,250 seconds or 1.18 hours. So 250 million years ago the day length would have been 22.82 hours. ...


13

In your comparison with raw eggs and milk cartons, the objects (and the liquid) inside are already at rest and you apply energy to rotate them. However, the entire earth is already rotating with comparably small external torques trying to slow it down. Back to your example, once you get the eggs spinning and try to stop them, they will continue to spin as ...


11

Not sure if I can add much to Kyle's comment, but I'll try. Looking closely, he starts with no angular momentum about the vertical axis - the take-off is "straight". Then he moves one arm behind himself and then extends it sideways - generating a torque about the vertical axis. By tucking his other arm in tightly, his body can now rotate. At the end of the ...


11

Ultimately, what's special about angular momentum is this: Look up in the sky. A certain set of physical laws pertain in that direction. Look to the north. A certain set of physical laws pertain in that direction. Look to the west. A certain set of physical laws pertain in that direction. Those physical laws: They're the same in all directions. There's ...


10

One of my favorite scientific papers of all times (mainly because it's rather bizarre) explains the basics of what's going on here. That paper is Kane & Scher, "A dynamical explanation of the falling cat phenomenon," International Journal of Solids and Structures 5.7 (1969): 663-666. To get even more mathematical, there's Montgomery, "Gauge theory of the ...


10

Since there is no friction, then it will not affect any other forces that may act on the car. The direction of wind blowing on the car may change its trajectory, as any driver will attest when driving in high winds. Turning the car wheels may have a slight affect on the resultant direction of the force. If the car has curved roof, then it may acts as ...


9

I physically understand it as the momentum of an object rotating around something given a certain position. However, I can't give a physical explanation to the formula. Why do we multiply the linear momentum by the position? Why does the angular momentum is a function of the position? 1) - Angular momentum $L = mv * r$ (p * r = arm of the ...


9

Yes. It turns out that your $T_L$ is equal to $-T/\omega$, where $\omega$ is the angular velocity and $T$ is the usual temperature. We normally work with the reciprocals of such quantities, and in the language of non-equilibrium thermodynamics we say that a gradient in $-\omega/T$ is the "thermodynamic force conjugate to" a flow of angular momentum. Within ...


8

If the ladder is slipping on the floor as well as the wall, then the point of rotation is where the two normal forces intersect. This comes from the fact that reaction forces must pass through the instant center of motion, or they would do work. In the diagram below forces are red and velocities blue. If the ladder rotated by any other point other than S ...


8

I think the solution has more to do with the tennis racket effect (see: http://physics.stackexchange.com/a/17507/392). Let me clarify the disk with hole in it has two stable axes of rotation and one unstable one. The unstable one is through the hole and the stable one is across (below in green) and normal to the disk. I have confirmed that without ...


8

Actually, seismic evidence indicates that Earth's liquid core rotates a little faster than the crust does. This is probably because the rotation-slowing effects of tides with the moon act more strongly on the surface than on the core. Jupiter, the other gas giant planets, and the Sun are all entirely fluid, are roughly the same age as Earth, and rotate. The ...


7

First of all it is a bit strange to express the change of Earths rotation in miles per second every 100 years, since the speed due to Earths rotation depends on your position on Earth. It would be better to express it as an angular deceleration, so for example in radians per second squared. But lets assume you mean the velocity at Earths equator, which has ...


7

Neither article that is quoted shows "$4.7 \cdot 10^{-4}$ miles per second". The Wikipedia article claims that a day grows longer by about $1.7$ milliseconds per century, that is say $86,400.0017$ instead of $86,400.0000$ seconds. Around the equator, the distance covered in a day is exactly $40,000$ Km (that's how the kilometre was initially defined). ...


7

There's another way to do this also, more akin to how spacecraft actually do it: Take a weight on a string, hold it up and spin it. You'll turn in the opposite direction. When you stop it you also stop turning. Of course this will produce an off-axis force that will be a real pain to deal with. Real spacecraft do it by means of a set of internal wheels ...


7

It is great that you "think differently" about problems - that is at the heart of all innovation. When it comes to the rotation of planets, you have to go back to the origins of the solar system: Planets are formed by accretion: a large cloud of debris starts to experience some gravitational pull, and as one "lump" becomes bigger than the others, it starts ...


6

The answer depends on what the symbols mean. The question does not make it clear how the symbols are defined. The most confusing quantity is $\omega_2$. How is this defined? Is it the angular velocity of the disc relative to the fixed lab axes or relative to the axle about which it is rotating (where this axle itself will be rotating at $\omega_1$)? Also ...


6

The Earth's rotation rate and the location of the rotation axis change over time. These collectively are called the Earth orientation parameters. On very short time scales, a day or less, the changes in the Earth orientation parameters result predominantly because of the ocean tides. On the scale of decades to a century or so, the dominant driver is exchange ...


6

Actually, your book is correct. Even if the most usual uses of angular momentum involve circular or rotating motion, this is not the general case. An object moving in a straight line has angular momentum in a reference frame in which the origin does not fall on the the line. To see this simply remember the definition of angular momentum ...


6

Surpringingly the top speed is not necessarily anything to do with friction, though friction will of course have some effect. A motor acts as a generator, i.e. if you turn a motor it will generate a potential difference just like a generator, and this potential difference (usually called the back EMF) is proportional to the motor speed. So if you connect a ...


6

Suppose the ramp wasn't there, then the trajectory of the object would the same as if it fell off a cliff: To get the equation of motion you simply note that the horizontal and vertical coordinates are given by (neglecting air resistance): $$ x = ut $$ $$ y = \tfrac{1}{2} g t^2 $$ So you can get the trajectory by substituting for $t$ to get: $$ y = ...


6

The moment of inertia is a rank 2 tensor not a scalar. You'll commonly see it written as a scalar, but this is because by choosing your axes to line up with the principal axes of the object the matrix representing the moment of inertia can be diagonalised: $$ {\bf I} = \left( \begin{matrix} I_{00} & 0 & 0 \\ 0 & I_{11} & 0 \\ 0 & 0 ...


6

I think I initially misunderstood the question. I now believe there are three components here: a rigid massless rod in the shape of a spiral; a massless spring that is wound around the rod in a frictionless manner; and a bead at the end of the spring. The entire system is anchored at the point A by a single nail - thus, the system is free to rotate about ...



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