## MCAT Physics and Math Review

**Chapter 1: Kinematics and Dynamics**

### 1.5 Newton’s Laws

Now that we have a clear understanding of force, mass, and acceleration, let’s examine how they relate to each other. While it is unlikely that Newton “discovered” gravity by having an apple on his head, he did record that he was indeed inspired by watching apples fall from trees. His observations about objects in motion and at rest are the basis for the branch of physics that we now know as mechanics. Newton’s laws, which are expressed as equations, concisely describe the effects forces have on objects that have mass.

FIRST LAW

**F**_{net} = *m***a** = 0

**Equation 1.15**

where** F**_{net} is the net force, *m* is the mass, and **a** is the acceleration.

*A body either at rest or in motion with constant velocity will remain that way unless a net force acts upon it.* This is also known as the law of **inertia**. Newton’s first law ought to be thought of as a special case of his second law, which is described next.

SECOND LAW

**F**_{net} = *m***a**

**Equation 1.16**

where** F**_{net} is the net force, *m* is the mass, and **a** is the acceleration.

What Newton’s second law states is actually a corollary of the first: *An object of mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector*. No acceleration will occur when the vector sum of the forces results in a cancellation of those forces. Note that the net force and acceleration vectors necessarily point in the same direction.

THIRD LAW

**F**_{AB} = –**F**_{BA}

**Equation 1.17**

This law is also known as the law of action and reaction: *To every action, there is always an opposed but equal reaction*. More formally, the law states that for every force exerted by object A on object B, there is an equal but opposite force exerted by object B on object A. For example, when you hit your hand against your desk, your hand exerts a force on the desk. Simultaneously, the desk exerts a force of equal magnitude in the opposite direction on your hand. Physical contact is not necessary for Newton’s third law; the mutual gravitational pull between the Earth and the Moon traverses hundreds of thousands of kilometers of space.

**MCAT Concept Check 1.5:**

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

1. In your own words, provide a description of Newton’s laws of motion:

1.

2.

3.