What is the intuition behind the right hand rule?

[Vay]

For example, in an angular rotation, the direction of the velocity of angular rotation can be found using the right hand rule. A disk rotating clockwise has angular velocity downward on the rotational axis.

 

Now, I want to ask, what does it mean by the angular velocity is downward? Isn't the angular velocity in the clockwise direction, so where does this downward direction come from? (Don't say, "it's because of right hand rule", because that's just begging the question).

Edited April 7, 2013 by Vay

[ewmon]

It's because of right hand rule ^{— Sorry, I couldn't resist !}

 

When you wrote that the angular velocity was "downward", I easily realized — using the right-hand "convention" — that the disc spinning clockwise had its axis vertical and that it spun clockwise while looking down from above. Otherwise, the axis could have been horizontal (as with the hands of a wall clock, where the angular velocity is into the wall) or vertical (as with the blades of a ceiling fan). If a ceiling fan is spinning clockwise as seen from below, then its angular velocity would be "upward".

 

You could have just as well used a left-hand convention in your example and said that the angular velocity was upward as long as everyone knew you were using that convention so they could correctly interpret the description you gave it (ie, upward).

 

There's another point I want to make, but I'm not remembering it well enough to explain it.

 

convention

n.

a general agreement about basic principles or procedures; also : a principle or procedure accepted as true or correct by convention

 

We live our lives by lots of conventions.

 

We put on our right blinker to make a right turn. It means, "Look out! I'm turning this way." The opposite convention would be to put on our left blinker to make a right turn. With such a convention, the left blinker means, "Pass me on this

side because I'm turning right."

 

If a young lady purposely ignores a guy, it would indicate under the most common convention that she's not interested in him. But, if he interprets it under an alternate and much less common convention to mean he's not trying hard enough, then his misinterpretation could get him into trouble.

 

With computers, HTTP (Hypertext Transfer Protocol) is a data transfer convention. Jpg, bmp, gif and so on are conventions that indicate how graphical data is written into, and read out of, a file. If you don't know the data storage format (aka, "convention"), you don't know how to write or read the file.

Edited April 7, 2013 by ewmon

[Vay]

So, the right hand rule is established purely for communication purposes; to tell the point of reference of the original observer?

Edited April 7, 2013 by Vay

[elfmotat]

The "right hand rule" is merely a simple way to determine the direction of a vector that is the product of one vector crossed with another. The cross product of two vectors is:

 

[math]\mathbf{A}=(a,b,c)[/math]

[math]\mathbf{B}=(d,e,f)[/math]

 

[math]\mathbf{A} \times \mathbf{B} = (bf-ce,cd-af,ae-bd)[/math]

 

So if, for example, [math]\mathbf{A}[/math] is the unit vector in the x-direction [math]\mathbf{A}=(1,0,0)[/math] and [math]\mathbf{B}[/math] is the unit vector in the y-directiontion [math]\mathbf{B}=(0,1,0)[/math], then the cross product is:

 

[math]\mathbf{A} \times \mathbf{B} = (0,0,1)[/math]

 

This is the unit vector that points in the z-direction. When translated into your fingers, your index finger represents [math]\mathbf{A}[/math], your middle finger represents [math]\mathbf{B}[/math], and your thumb represents [math]\mathbf{A} \times \mathbf{B}[/math].

[swansont]

So, to combine the two ideas above: the convention we use is that we have a right-handed coordinate system, i.e. if you draw the x and y coordinates, z will be in a direction given by the RH rule. And we apply the RH rule to situations involving cross products.

[ewmon]

Elfmotat explains the cross product of vectors that I couldn't remember.

[Vay]

Perhaps a better question is, In the case of looking downward on a disk rotating clockwise, what exactly is moving downward when right-hand rule is applied? I can learn to calculate it in vector notation, but I can never understand why it is calculated the way it does in three dimensional analysis.

Edited April 8, 2013 by Vay

[imatfaal]

Perhaps a better question is, In the case of looking downward on a disk rotating clockwise, what exactly is moving downward when right-hand rule is applied? I can learn to calculate it in vector notation, but I can never understand why it is calculated the way it does in three dimensional analysis.

Nothing is actually moving - we just name / designate certain thing in pre-agreed ways. Without conventions we would not be able to compare or use currents, E field, B fields etc. I need to know when you state something what it really means - and some (all?) expressions work just as well in one direction as they do in the opposite direction. It would be a ludicrous situation if we could both calcuate qv x B and yet get different but subjectively correct answers - to avoid this we specify a convention; the convention is in this case inherent in the arbitrary decision about the direction of the magnetic field.

 

The E field and the B field are to an extent arbitrary - the E field might have made more sense if it was positive in the direction an electron (the major charge carrier) moved but it was decided that it would be positive in the direction a test charge +q moves. The B field direction is defined by the righthand rule and the direction of the lorentz force. There is no underlying mystery - it's just a convention