Newton's First Law of Motion

This page describes Newton's first law of motion, the first of his three famous laws of motion published in his work Principia Mathematica.

The Main Idea

Newton's first law states that an object at rest will stay at rest and an object in motion will stay in motion with the same speed and direction of travel unless the object is acted upon by an unbalanced external force.

Newton's first law states that it is the natural tendency for objects to remain on their current course. The tendency of matter to obey this law is called Inertia, so it is also sometimes called the Law of Inertia.

A Mathematical Model

The first law states that if the Net Force acting on the object is zero, then its velocity [math]\displaystyle{ \vec{v} }[/math] will not change over time. Velocity is a vector, which has both direction and magnitude, therefore if the Net Force is zero, neither the direction or magnitude can be changing. In other words, if the net force acting on an object is zero, it will not accelerate.

This idea can be expressed in the following manner:

[math]\displaystyle{ \sum \mathbf{\vec{F}} = 0\; \Leftrightarrow\; \frac{\mathrm{d} \mathbf{\vec{v}} }{\mathrm{d}t} = 0. }[/math]

Newton's first law applies to:

1) Objects at rest ([math]\displaystyle{ |\vec{v}| = 0 }[/math]), which will stay at rest unless a nonzero force acts upon it.

2) Objects in motion ([math]\displaystyle{ |\vec{v}| \neq 0 }[/math]), which will continue to be in motion with the same velocity, proceeding in the same straight line, unless a nonzero force acts upon it.

Examples

Because of the qualitative nature of Newton's first law, some of these example problems are conceptual questions rather than mathematical calculations.

Simple

Question 1: Suppose you want to push a box across a table in a straight line at a constant speed. What force, if any, would you have to exert on the box? (Describe it qualitatively- not enough information is supplied for a numerical answer.)

Answer: The moving box would experience 3 forces (besides any you exert on it): gravity, normal force from the table, and friction with the table and air. Gravity points downwards, normal force points upwards, and friction opposes the direction of motion. Because of the nature of normal force, the normal force takes on whatever magnitude necessary to cancel gravity. The only unbalanced force is therefore friction. Since your objective is to keep the box moving in a straight line at a constant speed (that is, at a constant velocity), the net force acting on the box must be 0 according to Newton's first law. The force you exert should therefore balance the friction force by being equal in magnitude and opposite in direction.

Question 2: Is a change in position an indicator of interaction?

Answer: On its own, a change in position is not enough to indicate an interaction because an object can have a nonzero velocity (that is, have a changing position) even with no forces acting on it, so long as that velocity is constant. With some additional information, however, a change in position can indicate an interaction. For example, if an object is initially at rest and is later found at another position, its velocity must have changed and it must have been acted on by a nonzero unbalanced external force.

Medium

Question: A 16kg traffic light is suspended by two cables, each 22[math]\displaystyle{ ^\circ }[/math] from horizontal, as shown below:

What is the tension in each of the cables?

Solution: Because the traffic light is at rest and not accelerating, by Newton's first law, any forces acting on it must be balanced (that is, the net force acting on it must be 0). The forces acting on the traffic light are gravity and tension in the 2 cables. The horizontal components of the cables' tension forces must be equal in magnitude, or the traffic light would be accelerating to the left or the right. Combining that information with the fact that the two cables are inclined by the same amount leads to the conclusion that the tension in the two cables must be the same. Finally, we know that the combined vertical components of the two cables' tension forces must equal the traffic light's weight, or the light would be accelerating vertically. This allows us to create the following equation:

[math]\displaystyle{ 2T\sin(22) = 16*9.8 }[/math]

[math]\displaystyle{ T = \frac{16*9.8}{2\sin(22)} = 209.3 }[/math]N.

Difficult

(Requires knowledge of Static Friction.)

Question: Suppose there exists a car of mass 9000 kg that is moving at a constant speed of 90 m/s in an easterly direction. The car is being buffeted by a strong wind, which exerts a 1000N force on it in the northerly direction. From this information, you know that the coefficient of static friction between the road and teh car's tires [math]\displaystyle{ \mu_s }[/math] must be at least what value?

Solution: Because the car is travelling at a constant speed without changing direction, by Newton's first law, any forces acting on it must be balanced (that is, the net force acting on it must be 0). The forces acting on the car are gravity, the normal force from the road, the wind, and static friction with the road. Gravity acts in the downward direction, the normal force acts in the upward direction, the wind acts in a northerly direction, and static friction acts in a southerly direction. We know that the magnitude of the normal force must be equal to the magnitude of the gravitational force, or the car would be accelerating vertically. That is, the magnitude of the normal force [math]\displaystyle{ N }[/math] must be 9,000kg * 9.8m/s = 88200N. We also know that the magnitude of the static friction force must be equal to the magnitude of the wind force, or the car would be accelerating along the north-south axis. That is, the magnitude of the friction force [math]\displaystyle{ f_s }[/math] must be 1000N.

[math]\displaystyle{ f_s \leq \mu_s * N }[/math]

[math]\displaystyle{ \mu_s \geq \frac{f_s}{N} }[/math]

[math]\displaystyle{ \mu_s \geq \frac{1000}{88200} = .0113 }[/math]

Connectedness

Newton's first law is applicable to any situation where the net force on an object is 0 and its velocity remains constant. There are nearly limitless examples of such situations, as well as nearly limitless applications. A few can be found below.

Scenario: Tablecloth Party Trick

A classic demonstration of Newton's first law is a party trick in which a tablecloth is yanked out from underneath an assortment of dinnerware, which barely moves and remains on the table. The tablecloth accelerates because a strong external force- a person's arm- acts on it, but the only force acting on the dinnerware is kinetic friction with the sliding tablecloth. This force is significantly weaker, and if the tablecloth is pulled quickly enough, does not have enough time to impart a significant impulse on the dinnerware. This trick demonstrates Newton's first law because the dinnerware begins at rest and remains so because no significant forces act on it.

Scenario: Objects in Space

In space, some intergalactic objects exist so far away from other bodies of matter that gravitational forces acting on them are negligible in magnitude. These objects continue to move in a straight line at a constant speed for very long periods due to Newton's first law.

History

The nature of the tendencies of matter regarding motion has been the subject for much of human history. Aristotle (384–322 BCE) famously believed that all objects

This theory was originally discovered by Galileo who conducted experiments on the concepts of inertia and acceleration due to gravity. Galileo studied the movement of balls on smooth and rough surfaces, developing the idea of friction. Isaac Newton further studied these concepts and ideas and presented his 3 Laws of Motion. The first of these 3 laws, as we know, stated that an object in motion will stay in motion with the same speed and direction until an unbalanced force acts on it. And with the absence of friction or other forces, an object will continue moving forever.

From the original Latin of Newton's Principia: Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.

Translated to English, this reads: "Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed."

• Aristotle, the Greek who had an opinion on everything, believed that all objects have a natural place. Heavy objects wanted to be at rest on the Earth and light objects like smoke wanted to be at rest in the sky. He even went so far as to hypothesize that stars belonged only in the heavens. He thought that the natural state of objects was at rest and that nothing could keep moving forever without an external force. He did not believe that an object, without any external forces, could keep moving forever.

• Galileo, a more enlightened man, believed that although an outside force was needed to change the velocity of an object, no force was necessary to maintain its object. It could keep moving forever if nothing acted on it.

• Newton, who formally stated the law in the fancy language of Latin and whose name is attached to the very law, actually did nothing more than simply restate the law of inertia which Galileo had already described. He even gave the appropriate credit to Galileo, but to this day, we refer to this law not as Galileo's First Law, but as Newton's.

See Also

• Inertia
• Velocity
• Acceleration
• Newton's Second Law of Motion
• Newton's Third Law of Motion
• Galileo Galilei

Further reading or exploring

Science of NFL Football: https://www.youtube.com/watch?v=08BFCZJDn9w

Real world application of Newton's First Law: https://www.youtube.com/watch?v=8zsE3mpZ6Hw

Everything you want to know about Newton's First Law of Motion: http://swift.sonoma.edu/education/newton/newton_1/html/newton1.html

External links

NASA can help you understand: https://www.grc.nasa.gov/www/k-12/airplane/newton1g.html

References

http://teachertech.rice.edu/Participants/louviere/Newton/law1.html

Matter and Interactions: Modern Mechanics. Volume One. 4th Edition.

Page Created by: Brittney Vidal November 10, 2015 <-- For Credit

Page Edited by: Vivekanand Rajasekar November 27, 2015 <-- For Credit

Page Edited by: Raj Patel April 9, 2017 <-- Not For Credit

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