Newton's Laws of Motion

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In order to accurately describe how things move, you need to be careful in how you describe the motion and the terms you use. Scientists are usually very careful about the words they use to explain something because they want to accurately represent nature. Language can often be imprecise and as you know, statements can often be misinterpreted. Because the goal of science is to find the single true nature of the universe, scientists try to carefully choose their words to accurately represent what they see. That is why scientific papers can look so ``technical'' (and even, introductory astronomy textbooks!)

When you think of motion, you may first think of something moving at a uniform speed. The speed = (the distance travelled)/(the time it takes). Because the distance is in the top of the fraction, there is a direct relation between the speed and the distance: the greater the distance travelled in a given time, the greater is the speed. However, there is an inverse relation between time and speed (time is in the bottom of the fraction): the smaller the time it takes to cover a given distance, the greater the speed must be.

To more completely describe all kinds of changes in motion, you also need to consider the direction along with the speed. For example, a ball thrown upward at the same speed as a ball thrown downward has a different motion. This inclusion of direction will be particularly important when you look at an object orbiting a planet or star. They may be moving at a uniform speed while their direction is constantly changing. The generalization of speed to include direction is called velocity. The term velocity includes both the numerical value of the speed and the direction something is moving.

Galileo conducted several experiments to understand how something's velocity can be changed. He found that an object's velocity can be changed only if a force acts on the object. The philosopher René Descartes (lived 1596--1650, picture at left) used the idea of a greater God and an infinite universe with no special or privileged place to articulate the concept of inertia: a body at rest remains at rest, and one moving in a straight line maintains a constant speed and same direction unless it is deflected by a ``force''. Newton took this as the beginning of his description of how things move, so this is now known as Newton's 1st law of motion. A force causes a change in something's velocity (an acceleration).

An acceleration is a change in the speed and/or direction of motion in a given amount of time: acceleration= (the velocity change)/(the time interval of the change). Something at rest is not accelerating and something moving at constant speed in a straight line is not accelerating. In common usage, acceleration usually means just a change in speed, but a satellite orbiting a planet is constantly being accelerated even if its speed is constant because its direction is constantly being deflected. The satellite must be experiencing a force since it is accelerating. That force turns out to be gravity. If the force (gravity) were to suddenly disappear, the satellite would move off in a straight line along a path tangent to the original circular orbit.

A rock in your hand is moving horizontally as it spins around the center of the Earth, just like you and the rest of the things on the surface are. If you throw the rock straight up, there is no change in its horizontal motion because of its inertia. You changed the rock's vertical motion because you applied a vertical force on it. The rock falls straight down because the Earth's gravity acts on only the rock's vertical motion. If the rock is thrown straight up, it does not fall behind you as the Earth rotates. Inertia and gravity also explain why you do not feel a strong wind as the Earth spins---as a whole, the atmosphere is spinning with the Earth.

Newton's first law of motion is a qualitative one---it tells you when something will accelerate. Newton went on to quantify the amount of the change that would be observed from the application of a given force. In Newton's second law of motion, he said that the force applied = mass of an object × acceleration. Mass is the amount of material an object has and is a way of measuring how much inertia the object has. For a given amount of force, more massive objects will have a smaller acceleration than less massive objects (a push needed to even budge a car would send a pillow flying!). For a given amount of acceleration, the more massive object requires a larger force than a less massive object.

Newton also found that for every action force ON an object, there is an equal but opposite force BY the object (Newton's third law of motion). For example, if Andre the Giant is stuck on the ice with Tom Thumb and he pushes Tom Thumb to the right, Andre will feel an equal force from Tom pushing him to the left. Tom will slide to the right with great speed and Andre will slide to the left with smaller speed since Andre's mass is larger than Tom's.

Another example: an apple falls to the Earth because it is pulled by the force of the Earth's gravity on the apple and the acceleration of the apple is large. The apple also exerts a gravitational force on the Earth of the same amount. However, the acceleration the Earth experiences is vastly smaller than the apple's acceleration since the Earth's mass is vastly larger than the apple's---you will ordinarily refer to the apple falling to the Earth, rather than the Earth moving toward the apple or that they are falling toward each other.


acceleration force inertia
mass Newton's 1st law Newton's 2nd law
Newton's 3rd law velocity


Newton's 2nd law: Force = mass × acceleration: F = m × a

Review Questions

  1. What 2 things can change for an acceleration?
  2. If you give a bowling ball a push FAR away from any gravitational effects, what will it do? If you throw a feather (again far out in space) at the same speed as the bowling ball, how will its speed compare to the bowling ball after 5 minutes?
  3. Let's say you're twirling a ball on a string and the string breaks. What path does the ball take and why is that?
  4. How do you know gravity acts on an orbiting satellite?
  5. How does a force exerted on an object relate to the object's mass or acceleration? Given the same force will a boulder accelerate more than a regular marble? Why?
  6. Why would you need to apply more force to a bowling ball than a feather (far out in space) so that they would be travelling at the same speed after 10 minutes?

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last updated: 11 May 2001

Is this page a copy of Strobel's Astronomy Notes?

Author of original content: Nick Strobel