# Tag Info

69

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 ...

65

The Foucault pendulum is a great experiment which does demonstrate that the Earth is rotating, but it was only introduced in 1851. The Earth had been known to rotate for several centuries before that, probably stimulated by Copernicus and Galileo pushing the heliocentric model of the solar system during the 16th century. A couple of decades before Faucalt's ...

49

Foucault pendulum. I don't know how the ancients did it, but it is surely pure classical mechanics. The animation describes the motion of a Foucault Pendulum at a latitude of 30°N.

47

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 ...

26

It's a classical mechanics effect for sure although a really interesting one. Following links on "Dzhanibekov effect" one gets at Marsden and Ratiu's "Introduction to Mechanics and Symmetry" Chapter 15 Section 15.9 "Rigid Body Stability" treating this with use of the Casimir functions. From remark 1: A rigid body tossed about its middle axis will undergo an ...

22

The reason is that you have a boundary layer on the surface of the blade of the fan. On the frame of the blade (the blade moves with some velocity, but at the frame of the blade the air moves) the boundary layer starts from the surface of the blade where the fluids velocity is zero and as you move away from the blade, the velocity increases up to the value ...

20

Your explanation is right: an earthquake can't change the axis of rotation, relative to a given inertial reference frame -- that is, the axis of rotation doesn't change relative to the "fixed stars" as a result of the earthquake. What the earthquake does is to move material around within the Earth, so that the position of the rotation axis relative to any ...

20

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 ...

16

I think the Foucault pendulum is the best answer, but for the sake of variety I'll add another very interesting one: the equatorial bulge affecting the figure of the Earth. This is the "pancaking" of the planet due to its rotation. You can measure the geometry of the Earth without leaving its surface, and find that it is bulging in accord with your ...

15

Well, the angular momentum conservation is still the essence although it may be formulated in a different language. The top is spinning around a vertical axis and the spinning around this axis can't disappear. if the top decided to fall, the spinning would either disappear or would be replaced by a totally different spinning around a horizontal axis, and ...

15

Applying the brakes makes the wheel stop turning in relation to the bicycle's frame but not in relation to the road. The bike's center of mass (especially with a rider pressing against the handle bars) is higher than the hub of the front wheel. When the brakes are applied that mass has momentum toward the front of the bike that exerts a force on the front ...

14

What about this hypothesis: Dust sticks everywhere, but since the propeller cuts through a lot of air, it meets more dust particles. Thus, more dust sticks to the propeller than elsewhere. Evidence I (Mark) took photos my the fan my room to support Damien's hypothesis. The first photo is of the leading edge of the fan blade, which impacts a lot of air, ...

13

From conservation of angular momentum we have $(I+\Delta I)(\omega+\Delta \omega) = I\omega,$ or $$\frac{\Delta \omega}{\omega} = - \frac{\Delta I}{I+\Delta I} \simeq -\frac{\Delta I}{I}.$$ We make the following simplifying assumptions: The earth is a sphere of uniform density of mass $M$ and radius $R$. The building is constructed on the equator by ...

12

An indirect indication that the Earth rotates is the fact that the rotation varies over time. First of all, the orientation of the Earth's axis changes: long-term effects like precession and slow variations in the axial tilt, as well as small short-term variations like nutation. Precession was already known in the Ancient world (Hipparchus, Ptolemy,...) and ...

11

The system needs to conserve momentum. In both cases, the momentum is whatever m*v is for the bullet. Since it's the same in both cases, the bullet and block have the same vertical velocity. Mechanical energy is not conserved. The reason the block hit on the side has more kinetic energy is that the bullet converted less of its kinetic energy into heat upon ...

10

Wind doesn't actually touch the surface. You can see the same effect on a car: even if you move at speeds beyond 70mph, the dust doesn't get blown away. If you look closely, there is a boundary layer between the matter of the fan and the air around the fan. When you get closer to the fan blades, the air starts to move with the fan (the blade pulls it ...

10

No, it's caused by conservation of angular momentum. Reducing air resistance won't cause her (or anything else) to speed up without an external force. Like linear momentum ($m v$), angular momentum ($r \times mv$) is a conserved quantity, where $r$ is the vector from the center of rotation. For a skater holding a static pose, for each particle making up ...

10

There was some doubt about Lubos' answer (which I've accepted), so this is just a verification. I copied the method Lubos described and found the potential difference for an ellipsoid with different eccentricities. Sure enough, for an oblate spheroid, if you make the center-equator distance a fraction $e$ larger than the center-pole distance, the ...

10

Infinitesimal rotations don't commute exactly if you're accurate enough. An infinitesimal rotation may be written as $$\exp( i a A )$$ where $a$ is an infinitesimal "angle" and $A$ is a combination of generators. Such an object doesn't commute with the analogous object $\exp(ibB)$ in general. Instead,  \exp(iaA) \exp(ibB) = \exp(ibB) \exp(iaA) \exp(-ab ...

10

Well, if we make a quick estimate of the mass of a huge building. Let's say the building has a base of $100\times100 \;\text{m}^2$ and a height of $1500 \;\text{m}$, this is already substantially bigger than the current biggest building. Then we have a volume of $1.5\times 10^7\text{m}^3$. If we make the assumption, again very rough and on the high side, ...

9

Quite clearly this man’s theory is balderdash. A massive collision could change the tilt of the Earth’s axis, but that would be one hell of a torque. The collision would not be with an asteroid either, but with another planet that might be as big as Mars. Clearly nothing like this happened in recent geological history, though the Earth did suffer a ...

9

The source in the Einstein field equations is the stress-energy tensor, not the scalar mass-energy. Adding rotation will affect multiple elements of the stress-energy tensor. You can sometimes get rough estimates of effects in GR by using $E=mc^2$ and pseudo-Newtonian arguments, but sometimes these are way off. As an example where it's way off, two light ...

9

The blades of a ceiling fan are pitched out of plane slightly. As a result, when the fan spins, the blades push air either up towards the ceiling or down towards the floor. Which direction it pushes air is determined by the direction the fan is spinning, and the direction the blades are pitched. The usual convention is given by the right hand rule: if you ...

8

ZPM isn't the full answer. A combination of gyro and thrusters are used. Primarily they use Control Moment Gyroscopes (CMG) located in the Unity Module. Secondary options with more thrust are the Russian Control Thrusters on both Progress and Zvezda (means star) modules. The CMG's are quite heavy gyroscopes at about 600 lbs each. Inside the black ...

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

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 ...

7

The short answer is that there's no wind near the blade. This is called no-slip condition in hydrodynamics of viscous fluids. [Concession] It is actually more than that. There's minor van der waals sticking which contributes to this otherwise purely hydrodynamic phenomenon.

7

When it is spinning its angular momentum is quite high. By conservation of angular momentum the spinning top is then more stable against small torques like the action of gravity on the top. The angular momentum of the top is $J = I \omega$ where $I$ is the inertia tensor and $\omega$ is the Darboux vector, whose magnitude is proportional to the rotational ...

7

The answer to your question depends on precisely how it is interpreted. In my opinion, the clearest way of understanding a car driving on the road does in fact have the engine doing work on the car, but it is possible to define the system involved such that this is is not so. However, under this interpretation, the engine does no work on the car regardless ...

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