MCAT Physics and Math Review

Chapter 1: Kinematics and Dynamics

Introduction

A professor once said: Biology is chemistry. Chemistry is physics. Physics is life. Not surprisingly, this was the claim of a physics professor.

Walking into MCAT preparation, many students think of physics as the least applicable science to medicine, reflecting on calculus-heavy premedical classes. But even in the medical field, physics is all around us. When we treat patients at a rehab hospital, we often talk about motion, forces, and bone strength. An ophthalmologist may draw diagrams to help students better understand myopia and presbyopia. When we talk about mitochondria functioning as the batteries of the cell, we mean that fairly literally.

This first chapter reviews the three systems of units encountered on the MCAT: MKS (meter–kilogram–second), CGS (centimeter–gram–second), and SI (International System of Units). We’ll take a few moments to review the geometry of physics questions, especially vector mathematics. Next, we’ll move into true physics content as we consider kinematics—the equations that deal with the motion of objects—and Newtonian mechanics and dynamics—the study of forces and their effects.

1.1 Units

Before we begin our discussion of motion, we must define a consistent vocabulary for our discussion of physics throughout this book. Physics relies on the language of mathematics to convey important descriptions and explanations of the world around us. Yet those numbers would themselves be meaningless—or vague at best—without the labels of units.

REAL WORLD

Natural phenomena occur on many scales, as shown in Figure 1.1. We often assume that the fine details have little bearing on the larger scale of the universe, but the rapid inflation of the universe allows the infinitesimally small to affect the astronomically big.

Figure 1.1. Size of Natural Phenomena

FUNDAMENTAL MEASUREMENTS

Over the years, various systems of units have been developed for specific purposes. Some of these systems are commonly used in everyday life but rarely in science. The British or Imperial system (foot–pound–second or FPS) is used commonly in the United States but virtually nowhere else—not even in Britain. Basic units for length, weight, and time are the foot (ft), the pound (lb), and the second (s), respectively. Because weight, and not mass, is used, the British system later derived the slug as a unit of mass. The MCAT rarely—if ever—utilizes FPS in passages or questions.

The most common system of units is the metric system, which is the basis for the SI units used on the MCAT. Depending on the context of a passage or question, the metric system may be given in meters, kilograms, and seconds (MKS) or centimeters, grams, and seconds (CGS). SI unitsinclude the MKS system as well as four other base units, as shown in Table 1.1.

Quantity

Unit

Symbol

Length

meter

m

Mass (not weight)

kilogram

kg

Time

second

s

Current

ampère (coulomb/second)

A

Amount of Substance

mole

mol

Temperature

kelvin

K

Luminous Intensity

candela

cd

Table 1.1. SI Units

In each measurement system, there are base units and derived units. Base units are the standard units around which the system itself is designed. Derived units, as the name implies, are created by associating base units with each other. For example, the newton—a unit of force—is derived from kilograms, meters, and seconds:  . Table 1.2 contains examples of important derived units from each of the systems described above. Prefixes for metric units and conversions between metric and Imperial units are discussed in Chapter 10 of MCAT Physics and Math Review.

Quantity

FPS

CGS

MKS (SI)

Mass

slug  or blob 

   

Force

 

dyne 

newton 

Work and Energy

foot—pound (ft · lb)

erg 

joule 

Power

foot—pound per second

erg per second

watt 

Table 1.2. Derived Units in Various Systems of Measurement

At the molecular, atomic, or subatomic level, different units may be given that are easier to work with at such a small scale. For example, length may be given in ångströms (1 Å = 10–10 m) or nanometers (1 nm = 10–9 m). Energy on the atomic scale can be expressed in electron–volts (1 eV = 1.6 × 10–19 J), which represent the amount of energy gained by an electron accelerating through a potential difference of one volt.

MCAT EXPERTISE

While it is good to be aware of the various systems of measurement, the only system that you are required to memorize for the MCAT is the SI system.

MCAT Concept Check 1.1:

Before you move on, assess your understanding of the material with these questions.

1.    If the newton is the product of kilograms and meters/second2, what units comprise the pound?

2.    Order the following units from smallest to largest: centimeter, angstrom, inch, mile, foot.