Introduction

Our modern laws of motion come from Isaac Newton , an English scientist who worked in optics, mathematics and physics. His most significant work was accomplished over a period of two years while he was living at home because Cambridge was infected with the plague.
His work resulted in the notion of a clockwork universe in which everything was connected to a set of internal gears. It was thought that if one could understand the gears, he could understand everything else and could predict what would happen. LaGrange, a colleague, suggested that if a sufficiently powerful entity knew the position and energy of every particle in the universe at a given moment it could predict everything that would happen.
The study of motion is called mechanics. Newton's work is summarized into three laws which are stated in terms of force, uniform motion, and acceleration. Force will be defined later - let's look at the last two now.

If you have a Java enabled browser, then try this Introduction to Newtonian Mechanics

Go Back Click here to return to Laws of Motion menu

Velocity & Acceleration

Velocity

The book uses the term uniform motion ; the more common terms are speed and velocity. Here we will use the two terms interchangeably but in a stricter sense, the two are not. What is the difference?

In a more quantitative form,

v = average speed = (total distance traveled) / (total time) v =

x /

t (explain notation)
Ex. A car goes 65 miles/hour; the earth travels around sun at 67,100 miles/hour

This image shows the various components of an object's velocity as it moves through a curved path. Click on the image to see an animation of the trajectory.

For Practice

A car moves 60 feet in 2 sec. and then 30 ft. in the following 3 sec.

Q: What is the average speed during the first 2 sec.? A: 30 ft/sec
Q: During the following 3 sec.? A: 10 ft/sec
Q: During the entire 5 sec. interval? A: 18 ft/sec

Acceleration

Acceleration is a change of velocity in a given period of time. It can be either positive or negative. Explain. In quantitative form a = average acceleration = v/t.

This image demonstrates the acceleration and velocity vectors of a ball travelling in a circular path.

This image shows the vector along which the ball would travel if it left its circular path.

For Practice

A car starts from rest and after 12 seconds has a velocity of 60 miles/hr
Q: What is the acceleration of the car? A: 5mi/hr/sec = 7.33 ft/sec
A car traveling at 65 miles/hour comes to a complete stop in 6 sec.
Q: What is the acceleration of the car? A: -10.8 mi/hr/sec = -15.9 ft/sec

Go Back Click here to return to Laws of Motion menu

Newton's First Law (Law of Inertia)

Every body continues in its state of rest or of uniform motion in a straight line, unless it is compelled to change by forces impressed upon it.
Two concepts are implicit in this law:
1. inertia: the tendency of objects to continue what they're doing, i.e. a property of matter which causes it to resist changes in motion.
2. force: that which produces a change of motion.

Summary: There is a reason for every change of motion. For every acceleration there is a force. The question one must answer is: "What are the forces?"

Go Back Click here to return to Laws of Motion menu

Newton's Second Law

This law defines the relationship between force and acceleration. It says that the following relationship exists:
1. the greater the force, the greater the acceleration
2. the proportionality constant between force and acceleration is the mass.
If one accepts this, then the rest is intuitive.
Law is expressed as: F=ma Explain.

For Practice

Q: What force is necessary to produce an acceleration of 10 m/s in a body of mass 1 kg? A: 10 N
Q: What force is necessary to produce an acceleration of 10 m/s in a body of mass 15 kg?A: 150 N
Q: If a body of mass 10 kg is acted on by a force of 20 N, what is the acceleration?A: 2 m/s
Q: If a body of mass 80 kg is acted on by a force of 20 N, what is the acceleration?A: 0.25 m/s

Some Questions to Consider...

If you are riding in a car at 60m/hr and the car hits a wall, what happens to you? No seatbelts, air bag?
Which is worse? Car hits a wall or car hits another car going 60m/hr in opposite direction? Why?

This picture demonstrates that the force "pulling" the car around the circular path is a function of the mass of the car and its acceleration.

Go Back Click here to return to Laws of Motion menu

Newton's Third Law

What it says: For every force there is an equal and opposite force. For example, when you sit in a chair, the chair pushes up on you with an equal and opposite force to the one you exert on the chair. The same is true of rockets; they are pu shed forward by forcefully releasing gas backwards.

This image demonstrates graphically Newton's third law. We see that the equal and opposite force to the weight force (mg) is the y-component of the normal force. The x -component of the normal force has as its "equal and opposite" the x - component of t he friction force (not shown).

***This is the least intuitive of Newton's Laws - if you have a spring balance attached to wall and exert force of 10 units, etc.

Go Back Click here to return to Laws of Motion menu

Momentum

You know that it is more painful to be hit on the head with a baseball than with a ping pong ball. But mass is not the only important thing. It is more painful to be hit by a fast ball than by a ball dropped from a height of 1 inch. Remember: Both mass and velocity are important!

***Momentum is the name given to the product of mass and velocity:

momentum = p = mv

Important to Remember

This quantity is not directly related to Newton's three laws. It is more of a secondary quantity which can be derived from them.
It is important because if two bodies collide, the total momentum before is equal to total momentum afterwards. This means momentum is conserved. Ex. Two pool balls hitting.

Go Back Click here to return to Laws of Motion menu