Units

Units to Know

To start let’s look at the must know units on the MCAT and how units are nested inside of other units. Don’t worry about writing all of these down or trying to memorize them right now. There is an accompanying Anki deck that will help you memorize them and a downloadable summary available at the end of the module for quick reference.

Base Unit	Derived Unit	Base Units
Newton (N)	N/a	kgm/s2
Joule (J)	Nm	kgm2/s2
Electron Volt (eV)	1.6 x 10-19 J*	kgm2/s2
Watts (W)	J/s or Nm/s	N/a
Pascal (Pa)	N/m2	N/a
Coulomb (C)	A×s	N/a
Volt (V)	J/C	N/a
Ampere (A)	C/s	N/a
Farad (F)	C/V	N/a
Hertz (Hz)	N/a	1/s or s-1
Molarity (M)	mols/L	N/a
Area	N/a	m2
Volume	N/a	m3

In most cases, we will be dealing with the derived, rather than base units. On rare occasions it will make sense to break units all the way down, however, in those circumstances using an equation probably would have been easier.

Go ahead and practice breaking down units with this short quiz to test yourself on the units and how they nest into one another.

Recap: 5-Step Approach

Now that we are aware of the important units let’s look at a couple of examples to see how this technique can be applied to various calculation questions. We will begin by using the general 5-step approach covered in the last module. Before jumping into an example question review the 5-steps below:

1. Define the answer’s units or variable
2. Collect units or variables in the question stem
3. Generate an equation (if using)
4. Triangulate missing units
5. Arrange and solve.

Now let’s go ahead and apply our general approach to the following problem

A train must generate 500N of force to overcome friction and maintain a constant velocity of 30m/s. How much power does the train generate and how much energy does it consume in a 10-minute period?

A. 15,000 W; 6,000,000 J

B. 15,000 W; 9,000,000 J

C. 90,000 W; 1,500,000 J

D. 90,000 W; 9,000,000 J

1. Answer’s units: W = J/s = Nm/s and J =Nm
2. Given units: N, m/s, and minutes
3. Generate Equation: Not Relevant
4. Triangulation: Not Passage Based
5. Arrange and Solve Units Style

Using Units

The meat of this strategy starts with step 5.

To begin we will identify whether we are building up a unit or breaking a unit out. In this case, I know that I want a Watt (W), which isn’t contained in any of the other units so we will be building the W up.

Building Up

We build units by arranging our given units until they are equal to the unit of interest. In this question, I am given the units N and m/s so to get to a W = Nm/s I will multiply the force by the velocity and end up with a W as shown below.

500 N × 30m/s = 15,000 W (or Nm/s or J/s)

Breaking Out

We also need to solve for a second value an amount of energy consumed in joules. Here the Joule (J) is contained in the watt since W = J/s so we will end up breaking it out rather than building it up. To do that we will focus on canceling out the units we don’t want as we would a number, in this case, by multiplying by seconds or a unit of time.

15,000 J/s × # of s

We don’t have a value in seconds and will instead need to use a conversion to get minutes into the correct form. The key to recognizing this step is realizing that we are dealing with a unit of time instead of getting hung up on the exact units since we are often able to convert from one form to another easily.

15,000 J/s × 10 min × 60 s/1 min = 9,000,000 J

Making B the correct answer: 15,000 W; 9,000,000 J

 Sometimes the setup is really simple, and you don’t need to change any units around. You can simply use what you have been given and solve. Other times you might need to unpack the units multiple times to figure out how everything fits together. Take a look at the video below to see this strategy applied to a variety of questions before trying some practice problems on your own.

Worked Examples