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Newton's Laws of Motion Study Guide

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Updated on Sep 28, 2011

Introduction

From the previous chapters on physical quantities and their corresponding units, you now know that the unit for mass, kilogram, is a fundamental unit. Mass might also be called a fundamental quantity. It relates to motion, forces, and energy, and therefore basically to the whole field of physics. In the following lesson, we will discuss inertia, Newton's laws of classical mechanics that connect motion to forces, and conditions for an equilibrium or non-equilibrium situation when an object is subjected to two or more forces at the same time.

Inertia

Imagine a situation where you have to push some furniture around, for example, if you are moving to a new home. Although you might think that taking clothes out of the dresser drawers before moving the dresser is a waste of time, the reality is that the amount of effort you put into unloading the dresser is much less than the effort you would use to move the full dresser. What opposition do we encounter in the two processes of moving the furniture? It is the mass that makes the difference; it is the mass that causes the resistance. This resistance that an object has to motion is something we call inertia. Mass is the quantity that measures inertia, and the fundamental unit for mass is the kilogram (kg).

Motion on a straight trajectory is called linear motion. Later, we will study objects moving in a circular trajectory, and they too will exhibit inertia; in this case, called rotational inertia.

Newton's First Law of Motion

Newton's first law of motion, or the law of inertia, states that an object continues to stay at rest or move in a uniform linear motion as long as there is no resultant (net) action on it.

Newton's First, Second, and Third Laws of Motion

The idea of resistance to motion was formulated by Newton into what we now call the first law of motion or the law of inertia.

There are two important words in this definition: continues and resultant. To understand this law, you must work with these two words together. Resultant (net) action refers to the idea that there might be an action on the object, or two, or more. The importance is not in individual actions but in the total effect on the object. The other word, continues, refers to one of the two situations: rest or uniform linear motion. That is, the object will maintain, or continue, an identical state of rest or motion at all times if there is no external action.

Most objects around us, when left to act independently of engines, will not continue their uniform linear motion. Also, objects that might be at rest at one time can change their state and accelerate. The motion is a result of interaction, and the objects accelerate (speed up) or decelerate (slow down). The change in the state of motion is due to a resultant force. The relationship among the resultant force, the mass, and the acceleration is the subject of the second law of motion.

As you may remember, physical quantities can be scalars or vectors. In this case, mass is a scalar, but both acceleration and force are vector quantities. Therefore, the second law does not refer only to the proportionality but also to the direction of the acceleration, telling us that the acceleration and the resultant force are in the same direction. The expression of the second law is as follows:

a = , or

where a is the vector acceleration, F is the vector representing the resultant force, and m is the mass of the object. This equation defines also the unit for force: a newton, or N. As we replace the unit for acceleration (m/s2) and for mass (kg), we can find the unit for force to be kg . m/s2 = 1 N.

As with all vectors, force will be completely defined by value, unit, and direction. The direction of the net force will also give the type of acceleration; if a > 0 (a positive number is considered to be the direction of motion), then the object is accelerated, and if a < 0 (opposite to motion), then the object is decelerated (slowed down).

Newton's Second Law of Motion

The acceleration of an object is directly proportional to the resultant (net) force and inversely proportional to the mass of the object.

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