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2004-G: Dimensional Analysis 2: Simplifying Dimensions of Quantities

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2004-G: Dimensional Analysis 2: Simplifying Dimensions of Quantities

BACK to Ladder Unit Conversion and Dimensional Analysis

Each of these unit can be written in terms of base unit:

Symbol
Quantity
Unit
Special Name of Unit
\( t \)
time
seconds (s)
seconds
\( m \)
mass
kilograms (kg)
kilograms
\( x \) or \( \Delta x \)
position or displacement
meters (m)
meters
\( v \)
velocity
\( \frac{\text{m}}{\text{s}} \)
none
\( a \)
acceleration
\( \frac{\text{m}}{\text{s}^2} \)
none
\( F \)
Force
\( \text{kg} \cdot \frac{\text{m}}{\text{s}^2} \)
Newtons (N)
\( p \)
momentum
\( \text{kg} \cdot \frac{\text{m}}{\text{s}} \)
none
\( K \) or \( U \)
Kinetic Energy or Potential Energy
\( \text{kg} \cdot \frac{\text{m}}{\text{s}^2} \)
Joules (J)

For each of the following quantities, write the unit in terms of meters, kilograms, and seconds.

Mass vs. Meters

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Practice

For each of the following combinations of quantities, determine the unit in terms of meters, kilograms, and seconds. The steps are:

  1. Write each quantity in terms of meters, kilograms, and second.
  2. If a quantity is in the numerator, add its unit in the numerator. If it is in the denominator, add its unit in the denominator.
  3. If a quantity is raised to some power, raise its unit to that power.
  4. Simplify the combination of unit, as in a previous pod.
  1. \( \frac{\left( \Delta x \right) a }{v^2} \)
  2. \( \frac{\left( \Delta t \right) v^3 }{\left( \Delta x \right) a^2} \)
  3. \( \frac{m^2 \left( \Delta t \right)^5}{v^3} \) Note that \( m \) stands for mass here, not meters!
  4. \( \frac{a^3 v^2}{m^2 \left( \Delta x \right)^4} \)

Video Resources

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