# Tag Info

### Why do rain drops fall with a constant velocity?

Here is a slightly different way to think of this. If the net force is zero, the acceleration of the droplet is zero- even though its velocity is not zero. With the acceleration zero, the velocity ...
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### Why does a system try to minimize its total energy?

The anthropomorphic formulation "tries to" is misleading. Under the effect of ambient noise, matter explores the possible configurations around its current state: e.g., two single hydrogen atoms ...
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### Why is it easier to handle a cup upside down on the finger tip?

Take a look at this picture of a cup slightly out-of-balance : In case (A), generated torque is directed out of your reference axis and in case (B) - towards your reference axis. So in case A), you ...
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### Why do most office chairs have 5 wheels?

Consolidating some of the points made in the answers to the question you linked, and comments: When constructing a chair, 4 legs is easy when you use traditional (wooden) construction - 90 degree ...
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### Why do things cool down?

You exchange heat with the objects around you. If the objects around you are hotter than you, you'll heat up. If the objects around you are cooler than you (neglecting the heat you're generating due ...
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### Why (does/we assume) gas exert same pressure everywhere in a closed container?

An imbalance of pressure would itself cause an internal flow in the gas. So if the gas has reached equilibrium the pressure must be the same everywhere. The above is for a gas in ordinary ...

### Why do rain drops fall with a constant velocity?

If the forces on an object add to zero (in an inertial reference frame) it experiences zero acceleration and hence moves with a constant velocity (but not necessarily zero velocity). Thus, this is a ...
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### How is quantum mechanics consistent with statistical mechanics?

The question doesn't make sense, as not every system has to be in thermal equilibrium. The argument you're making works for classical mechanics too. "Consider a ball lying on the ground." "That's ...
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### How can I prove that a state of equilibrium is unstable?

In the centre of a bowl there is equilibrium. Put a ping pong ball in it. If this ball is ever shaken slightly away from equilibrium, it will immediately roll back. A "shake-proof" equilibrium is ...
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### Why does a system try to minimize its total energy?

This is a consequence of the second law of thermodynamics, which states that In a closed system with fixed internal energy (i.e. an isolated system), entropy is maximized at equilibrium. It can ...
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### Is thermodynamics only applicable to systems in equilibrium?

It entirely depends on what you think "thermodynamics" is. The traditional idea of thermodynamics dealing with systems whose macrostate can be fully described by e.g. temperature, pressure and volume ...
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### If the Earth is in constant motion then why do we say that an object is in a state of rest?

"A state of rest" is a relative term. Relative means - measured in comparison to the things around it. When you sit in a train and sip from a cup of coffee, you can do so because the cup is still ...
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### Why doesn't an object, despite having a non-zero potential energy stored in it, fall by itself from the elevation?

It is wrong to think potential energy is stored in the object. The earth pulls the object down, but the object pulls the earth up. They share the potential energy. The object fails to fall down ...
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### Earth as a perfect sphere and an object trying to stand still

Indeed, you need friction. Otherwise this object will slide to equator just as you expect. In fact, all the objects will slide there to form equatorial bulge and eventually the sphere will be turned ...
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### Why do rain drops fall with a constant velocity?

This is Newton's first law: if the force vanishes the velocity is constant. Constant but not necessarily zero. The resistive force increase as long as speed increases. When it is equal to the ...
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### Why does a system try to minimize its total energy?

This is really a statistical effect, as pretty much all of thermodynamics. You have two free hydrogen atoms. They tend to move around the space they have, and when conditions are favourable (there's ...
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### Why is it easier to handle a cup upside down on the finger tip?

Maybe because when the cup is the right way up, it’s centre-of-mass is above the point on your finger meaning that as your finger tries to balance the cup any small motion will generate a torque about ...
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### Why does a system try to minimize its total energy?

I'm going to take a slightly different approach and say it's because we defined energy to make it so. In other words, systems "try" to find the lowest energy state because energy is a concept humans ...
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### Is ergodic hypothesis in contradiction with the notion of equilibrium?

You have to be careful to distinguish between microstates and macrostates. Thermodynamic equilibrium is a macrostate which consists of a mixture of all possible microstates of energy $E$ weighted by ...
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### Why (does/we assume) gas exert same pressure everywhere in a closed container?

It depends on the resolution of your measuring device. A gas contains on the order of $10^{22}$ molecules zipping about. The pressure on a wall of the container is due to the tiny force applied by ...
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### Thermodynamic reversible process

This is a very interesting, important and at the same time subtle matter which is useful not only in thermodynamics, but other areas as well, and not everyone quite understands it. First off, two ...
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### How are the Lagrange points determined?

Sketched proof of all possible Lagrange points: Consider first the 2-body problem. Deduce that possible Lagrange points must lie in the orbital plane (because a probe will always be gravitationally ...
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### Facing a paradox: Earnshaw's theorem in one dimension

Your example does not contradict Earnshaw's theorem for electrostatics, because it rules out stable equilibrium in a region without charge, possibly containing fields made by charges outside that ...
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### Objects falling from table

If the centre of gravity of the object is vertically above the edge of the table then the object is in equilibrium. However, this equilibrium position is unstable (like a pencil balanced on its point) ...
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### Understanding the Jacobian Matrix

Let us look at a one-dimensional example: Recall that $f(x) = \dot{x}$, so $f$ encodes the time evolution of $x$. If $f < 0$, then $x$ will move to the left. If $f > 0$, then $x$ will move to ...
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### Does zero net force imply zero net torque?

does it also leads to ... No, it doesn't. A simple Counterexample: Consider the figure below (the bar $\textrm {AB}$ and forces $F$ are on a plane parallel to $\textrm {xy}$ plane) We have \$\Sigma ...
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