Mathematical equations used in science contain dimensions such as meters or seconds. Dimensional analysis is a tool for verifying these equations.^{[1]} The dimensions, or units of measure, on both sides of an equation must agree for an equation to be valid.
A dimension is not the same as a unit of measure. A unit of measure may have multiple dimensions such as m/s (velocity), or m/s^{2} (acceleration).
Unit of Measure | Symbol | Dimension |
---|---|---|
distance | m | meters |
km | kilometers | |
ft | feet | |
mi | miles | |
time | s | seconds |
h | hours | |
ms | milliseconds | |
mass | kg | kilogram |
velocity | m/s | meters per second |
mi/h | miles per hour | |
km/h | kilometers per hour | |
acceleration | m/s^{2} | meters per second squared |
mi/h^{2} | miles per hour squared | |
km/h^{2} | kilometers per hour squared | |
energy (joules) | kg·m^{2}/s^{2} | kilogram meters squared per second squared |
force (newtons) | kg·m/s^{2} | kilogram meters per second squared |
Table 1. Underlined dimensions are the SI (Système Internationale) units. Use of SI System units is preferred over other, non-SI units. |
The variables in this understanding check have the following meanings:
Check the validity of each equation using dimensional analysis. Then click the 'Click for answer' button to see the correct answer.
1. | d = t·a | Click for AnswerInvalid. The dimensions are m = s·m/s^{2} which simplifies to m = m/s. |
2. | g = f·d | Click for AnswerValid. The dimensions are kg·m^{2}/s^{2} = (kg·m/s^{2})·m which simplifies to kg·m^{2}/s^{2} = kg·m^{2}/s^{2}. |
3. | v = f·t/d | Click for AnswerValid. The dimensions are m/s = (kg·m/s^{2}·s/m which simplifies to m/s = m/s. |
4. | m·f = g | Click for AnswerInvalid. The dimensions are kg·(kg·m/s^{2}) = kg·m^{2}/s^{2} which simplifies to kg^{2}·m/s^{2} = kg·m^{2}/s^{2}. |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
All Math Words Encyclopedia is a service of
Life is a Story Problem LLC.
Copyright © 2005-2011 Life is a Story Problem LLC. All rights reserved.
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License