Unit 2 - Problem 8 Dimensional Analysis

 

Definition

• Dimensional Analysis is the process of determining the M (mass), L (length), and T (time) exponents for a given variable.
• For example, velocity is equal to length raised to the power of one divided by time raised to the power of one. Mass is not involved so it's exponent is zero making it's value 1 and thus not reported. Consequently, we have: $$V = \frac{length}{time} = \frac{L^1}{T^1} = L^1 * T^-1$$
• For an MLT value = 1,-1

Unit 2 - Problem 8 asks:

• What is the MLT for: $$\frac{h^2}{ m x^2} = E  = m c^2$$
• So solving for h:
• $$h^2 = (m * x^2) * m * c^2$$
• $$h^2 = m^2 * x^2 * c^2$$
• $$h = m * x * c$$
• Note that: x = L(ength); and c(velocity, i.e. speed of light) = L/T
• Which in MLT I think means:
• $$MLT = M^1;L^1;(\frac{L}{T})^1 = M^1;L^1;(L^1,T^−1)$$
• $$MLT = M^1;L^2:T^−1$$
• Making MLT parameters = 1,2,-1

Another use for MLT

• Is shown by MIT Professor Lewin in this video around 22 minutes
• Units, Dimensions, and Scaling Arguments