Newton's First Law of Motion

Claimed by Raisa-Claire Aghomo (Fall '23)

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.

Scenario: Turning car

You have probably experienced a situation in which you were driving or riding in a car when the driver takes a sharp turn. As a result, you were pressed against the side of the car to the outside of the turn. This is the result of Newton's first law; when the car changed direction, your body's natural tendency to continue moving in a straight line caused it to collide with the side of the car (or your seatbelt), which then applied enough normal force to cause your body to turn along with the car.

History

The nature of the tendencies of matter regarding motion has been the subject of much thought throughout human history. Aristotle (384–322 BCE) famously believed that all objects have a "natural place" towards which they tend: heavy objects belong on the earth and therefore tend to move downwards, while lighter substances such as smoke belong in the sky and therefore tend to move upwards. Once an object reached its natural place, Aristotle believed, it would remain there at rest. Aristotle believed objects could not continue to move forever without being acted on by a force to keep it in motion, which is consistent with any observations he could have made on the surface of the earth, although today, we know this to be the result of Friction.

Galileo Galilei (1564-1642), who studied the motion of celestial bodies, was the first to propose that perpetual motion was actually the natural state of objects, and that forces such as friction were necessary to bring them to rest or otherwise change their velocities. Galileo performed an experiment with two ramps and a bronze ball. The two ramps were set up at the same angle of incline, facing each other. Galileo observed that if a ball was released on one of the ramps from a certain height, it would roll down that ramp and up the other and reach that same height. He then experimented with altering the angle of the second ramp. He observed that even when the second ramp was less steep than the first, the ball would reach the same height it was dropped from. (Today, this is known to be the result of conservation of energy.) Galileo reasoned that if the second ramp were removed entirely, and the ball rolled down the first ramp and onto a flat surface, it would never be able to reach the height it was dropped from, and would therefore never stop moving if conditions were ideal. Galileo was essentially the first person to propose the idea that we now know as Newton's first law.

Isaac Newton (1643-1727) confirmed Galileo's idea with his own experiments and published it along with his 2 other laws in his 1687 work Principia Mathematica. Although he gave credit to Galileo, today the law is known by Newton's name.

Newton's first law appears in Principia (which was written in Latin) as follows:

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."

See Also

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

External links

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

NASA page on Newton's first law: https://www.grc.nasa.gov/www/k-12/airplane/newton1g.html

References

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

http://education.seattlepi.com/galileos-experiments-theory-rolling-balls-down-inclined-planes-4831.html

https://science.howstuffworks.com/innovation/scientific-experiments/newton-law-of-motion2.htm

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