Scope, Sequence, and Coordination
A Framework for High School Science Education
Based on the National Science Education Standards
Inertial Mass, Weight, and Newton's Second Law of Motion
Dynamics: Newton's Laws of Motion
Kinematics describes how things move but not why. With an understanding of kinematics, students can describe motion of various kinds. But why do objects move in ways that they do? What accounts for the changes in their motion? This is called dynamics.
Galileo’s law of inertiaCan object at rest remains at rest, and one in motion in a straight line at constant speed continues in that same motionCis equivalent to Newton’s first law. Students must observe that to change either the speed of an object or its direction of motion, there must be an interaction of the object with something else. That interaction is called a force. In its simplest description, force is just a pull or push, but in general it is a measure of the interaction between the objects. Force can be defined operationally in terms of the stretch of a linear spring. Objects can be made to speed up, slow down, or change their direction of motion by means of an unbalanced force, i.e., a net force.
Students are familiar with mass as something proportional to the amount of substance and as something they measure with a balance. The acceleration of an object is inversely proportional to its mass when a net force acts. The property of a mass resisting changes in motion is called inertia. Sometimes people refer to gravitational mass as the kind measured on a balance and inertial mass as the kind that opposes acceleration. Although these two kinds of mass need not be the same, Einstein postulated that they are equivalent, and all subsequent experiments have verified this equivalence.
Newton’s second law, F = ma (where F must be the net force), expresses the relationship between the net force acting on a mass and its acceleration. When considering forces, care must be taken to identify all of the forces acting upon that object, and the sum of these forces must be a vector sum. This vector sum must be used to find the resulting vector acceleration.
In the process of identifying forces acting on an object, we encounter forces acting on that object and forces it exerts on other things. This observation leads to another of Newton’s laws, Newton’s third law of motionCforces come in pairs, sometimes expressed "for every action there is an equal and opposite reaction." If you push on something, it pushes back on you with an equal and oppositely directed force. Newton’s laws allow us to predict the motion of an object if we know the forces acting on the object and its initial motion. We need only find the acceleration, then use kinematics to describe the motion.
Since there is a constant acceleration of freely falling bodies close to Earth’s surface, with g as the value of that acceleration, there must be a constant force. This force is called the weight of the body and is given by w = mg. The fact that Earth is not touching the falling body until it hits the ground illustrates another important idea, force acting at a distance but not touching.
An object moving in a circle (even at a constant speed, since the direction of motion is continuously changing) is accelerating, as we have previously shown, so there must also be a center-directed forceCa centripetal force. And some source of this centripetal force must be present. In the case of uniform circular motion, the force produces only a change in direction, not a change in speed. This motion is an example of what happens when a force is applied at right angles, or orthogonal, to the velocity. When two orthogonal forces act on an object, the change in motion caused by one force is independent of the change in motion caused by the other force.
Gravitational mass, force exerted by things touching or by things acting at a distance
Inertial mass, newton as a unit of force, net force or unbalanced force, action force, reaction force, weight as a force
Normal force, force equilibrium, resistive force (by contact at rest or by rubbing and plowing through)
Vector force, free-body diagram, orthogonal forces (forces at right angles to each other and their effects on motion), centripetal force (and source of a given centripetal force, i.e., gravity, contact, friction, electric, magnetic)
Whenever two objects interact with each other (regardless of the source of that interaction), they both accelerate during the interaction. Furthermore, during the interaction the ratio of the magnitude of the two accelerations is equal to the reciprocal of the ratio of their masses. This means that during that interaction, each object accelerates by an amount that is inversely proportional to its mass. It is also observed that these accelerations are oppositely directed.
Newton recognized that the observed empirical relationship of two interacting objects, m/M = A/a, equivalent to ma = MA, is independent of the nature of the interaction. That interaction was therefore called a force. Newton=s law, using the concept of force for the interaction, is a theory expressed by F = ma. Similarly, Newton=s first law is merely a special case of F = ma, when the net force is zero. In that case, the acceleration must also be zero, which means that the object is at rest or moving with a constant velocity. Newton=s third law expresses the character of the accelerations of interacting objects by recognizing that the two forces, each acting on the other, must have the same value but be oppositely directed.