what is R.M.S velocity?

Answer 1

R.M.S. is a frequently used term for the root-mean square voltage or current in a.c. circuits.
You would have an R.M.S. velocity if you are talking about the motion of gas molecules for instance.

Answer 2

Suppose a sphere containing N molecules having equal masses but different velocities
v1, v2, v3.....and vN.

The velocities may have any value and may have any direction.

However, we can resolve all the velocities into there mutual perpendicular directions.

In any direction there will be positive as well as negative directions for the components.

The mean of such velocities may, some times, be equal to zero.

But the sum of their kinetic energies is never zero.



Considering the kinetic energy of all molecules, we need not take the positive or negative sign, because the total kinetic energy is only ½ m (v1^2 + V2^2 +V3^2 .......VN^2).

The mean kinetic energy of each molecule is
½ m (v1^2 + V2^2 +V3^2 .......VN^2) / N


Let the value of

(v1^2 + V2^2 +V3^2 .......VN^2)/N = S

S = sum of the squares of velocities / number of molecules.

Or S is the mean "square velocity."

The mean kinetic energy of each molecule is

½ m S

This can be written as ½ m {√ S} ^ 2.

√ S} is now defined as the square root of the mean square velocity.


The square of the “root mean square” is the mean square.

Mean square multiplied by total number is
the sum of the individual squares.

To find the sum of the individual squares of certain quantity we simply multiply the mean sqaure with the total number.

And Mean square is square of R.M.S

Answer 3

Its used as a way to calculate an 'average' of the velocites, taking into account their +/- values. Vrms = sqrt(the average of the sum of the squares of the velocities). You use the same idea for calculating stdrd devns or when calculating a 'mean' value for a signal using integration when its time averaged value over a cycle would be zero (eg Vrms='peak'V/sqrt2)

Answer 4

Only R.M.S. I'm familiar with deals with AC voltage values. It stands for 'root-mean-square.'

Answer 5

If it is defined as sqrt(|v|^2), then it is more commonly referred to as "speed".