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.