Question

I am having trouble understanding a physics statement. "We shall refer to the dimension of base Quantity by the Quantity itself" Example : dim length = length = L / dim mass = mass = M

Are they referring to the the geometric shape of mass or length the at a point in space? How can a measurement have dimensions?

Answer 1

from my math dictionary by Clapham and Nicholson:" In mechanics, physical quantities can be described in terms of basic dimensions of mass M, length L, and time T, using positive and negative indices. For example, the following have the dimensions given: area, L^2; velocity, LT^-1; force, MLT^-2, linear momentum, MLT^-1; energy, ML^2T^-2; and power, ML^2T^-3. The notation has similarities with that of SI units."

I've come to think of dimension as being just another variable, but the mechanics definition seems a bit more structured (using just L, M, and T). This allows a generic kind of label that covers all possible variations that result from different measurement systems. For velocity I frequently used meters per second, but my car says miles per hour and something flying through space might be measured in kilometers per second; though they are all L/T .

Answer 2

I could be mistaken but i think this is a mesh of two statements.
"We shall refer to the dimension of base Quantity by the Quantity itself"
Is the result of a quantity that has no dimension.
e.g. How many 10 meter segments do you cross in a 100 meter dash? 10 (no dimension)

Answer 3

The question is from classical mechanics(2010) from MIT. I think you are both right in a way. From what I gather they are talking about if the base quantity of length is a meter then they just refer to it by L. Since the meter=length. So i guess the measurements components are referred to as length. Instead of dimensions they should have said components. Like finding the distance of a meter is the movement of light over a specified amount of time. Time=Seconds=Certain number of cycles of electromagnetic radiation emitted by cesium atoms as they make transitions between two designated quantum states. So using that measurement of oscillations with the distance speed of light travels within so many oscillations will give you distance. Mass = 39mm diameter and height of a metal alloy that is 90% platinum and 10% iridium.