One bottle holder:how it works?

What we have here is a free standing piece of wood carrying a bottle of water or wine. In order this structure to stay still,obviously it should not tip over.

 No, it's not magic. Its equilibrium like the man walking on a tight rope, but far less dangerous.

There is a physical quantity which ranks how effective is a force in rotating an object. It is called moment or torque of the force.
Torque (τ)  is defined as the magnitude of the force (F) times the distance (d) between the force's line of action and the pivot (the point,  or shaft on which the object turns or oscillates)


If an object does not rotate then the total or net torque (τ_net) of all the forces exerting on it should be zero.It's worth emphasising that the net torque should be zero for all possible pivots, since if it was not for one point then definitely there would be rotational motion around this very point).

Three forces are exerted on our one bottle holder system:
the wood's weight (w1), the weight of the bottle and its content (w2) and the ground reaction force N.

The point of application of the weight of an object is called center of gravity.  We can find where the center of gravity of an object is. For example, you can determine where your pen's center of gravity using balance.Therefore we can assume that we know the centers of gravity for both the bottle and the wood and they are P and O respectively.


Although the center of gravity is well defined and unique for an object, the point of application of the ground reaction force N can be defined but it is not unique. Let's call it Q and try to find where it is.

Since for equilibrium, the total torque should be zero for any pivot, let's refer to the point Q

• The moment of w₁ is -w₁d (negative since it contributes to clockwise rotation -with respect of Q).
• The moment of w₂ is +w₂d (positive since it contributes to anticlockwise rotation -with respect of Q).
• The moment of N is zero since its distance from Q is zero.

Therefore using equation 1 we can determine the position of Q.

What if the position of Q , as it is  found above, does not belong to the area of touch between the wood and the table?
The answer:
Our one bottle holder will tip over!
Why?
Because N is a contact force and as such it should have a point of application within the area of touch. If the appropriate location for Q is outside the basis of our construction then we deduce that the current 'area of touch' is not enough to prevent our object from tipping over.

OUR LIGHT MILL IN ACTION

DESCRIPTION

“The Crookes radiometer, also known as the light mill, consists of an airtight glass bulb, containing a partial vacuum. Inside, a set of vanes is mounted on a spindle. The vanes rotate when exposed to light, with faster rotation for more intense light, providing a quantitative measurement of electromagnetic radiation intensity.”

http://en.wikipedia.org/wiki/Crookes_radiometer

EXPLANATION

The motion of the air molecules in the radiometer from the hotter (black) to the colder (silver) surfaces of the vanes contributes to the rotation of the vanes. Molecules hitting the black side get heated up slightly and bounce off with higher energy. Due to the momentum conservation, this causes the vanes to recoil in the opposite direction. 

 Certainly this is a simplistic way to explain how solar radiometer works. The full detailed explanation was given by Reynolds in 1879. He used the term “thermal transpiration”. Let's try to explain a little bit more.  When the solar radiometer is placed under the sunlight, heat is being introduced in the form of light. Each of the four vanes has a silver

reflective side and darker black side. That  darker black side tends to  absorb light and hence heat which means we  have one side of the vane  a bit hotter than  the other side. However,nature likes to even things out by sending colder air on the silvery side around to the darker side

cool it off and  when it does that the balance of the gases changes.Air pressure builds up on the darker side while decreasing on the silvery side . As the cool air moves air particles move around to the warmer side and sometimes they displace some the warmer molecules which go to the other site. Now by definition warmer air molecules have more energy and are more excited , so they strike the vane with more speed. They  actually strike the black side to the vane  while on the other side there is  very little resistance because of the lower air pressure there. So the vane spins  around with the dark side leading.

Note that the first explanation made by Crookes himself, was based on the air pressure fact.  However, while light does exert a pressure, it's too tiny to cause the effects seen in the radiometer. Moreover, if this was true, then the reflective side of each one vane

should have been pushed along and the vane would have spined

in the opposite than the observed direction.

Uphill rollers: some double cones and a pseudosphere.

 The "uphill roller" is a physics demonstration first reported by the English Mathematician William Leybourn in 1964. In the original version, a double cone placed on two divergent inclined ramps appears to roll uphill, apparently violating the laws of physics.
The uphill roller is an example of the center of mass of an object descending under the influence of gravity.




Nikos Kassastogiannis, an inspired woodworker and an invaluable friend of mine made a nice wooden demonstration of the uphill roller on my request. You can watch the demonstration in the following video. Nikos  didn't only make the double cones I asked him to, but he also made a brilliant pseudosphere which you can watch in the video to oscillate before it reaches its equilibrium.

A pseudosphere is a surface with a constant negative Gaussian curvature. Revolving a tractrix of radius r about its asymptote generates this surface. Although the resulting surface has an infinite extension along its central axis, it has finite area ,exactly the same  as a sphere of radius r, and half its volume. The pseudosphere played an important mathematical role in the acceptance of non-euclidean geometry.

If this video whetted your appetite for more information, here they are some links to explore.
1.  A mechanical paradox or, a new and diverting experiment by William Leybourn

2.  "Pleasure with profit:: consisting of recreations of divers kinds, viz. numerical, geometrical, mechanical, statical, astronomical, horometrical, cryptographical, magnetical, automatical, chymical, and historical. Published to recreate ingenious spirits; and to induce them to make farther scrutiny intor these (and the like) sublime sciences. And to divert them from following such vices, to which (in this age) are so much inclin'd" by William Leybourn"

3. Defying gravity: the uphill roller.
4. Nikos Kassastogiannis, handmade wood