Dynamics Concepts

Dynamics is the scientific study of forces that make things move (there is another study of forces, called statics, that deals with forces that affect things but don't move them).  When physicists began to apply the science of dynamics as developed by Isaac Newton, it caused a revolution in science and technology.  This is one of the most significant events in the history of civilization.  Consult a history book or teacher for more info.

• A force is a push or a pull.

• Physicists identify four fundamental forces that affect matter in the universe.  Gravity, the electromagnetic force, the strong nuclear force, and the weak nuclear force.

• Gravity is an attractive force between any two objects with mass.

• The strong nuclear force holds atomic nuclei together.

• The weak nuclear force acts in the radioactive decay of some "weakly-interacting" particles.  It has (relatively recently) been unified with the electromagnetic force.

• The electromagnetic force concerns the attraction between electrons and protons, and the repulsion between electrons and electrons, or the repulsion between protons and protons.

• Forces that affect objects in our everyday experience may be the result of physical contact between two or more objects, or of non-contact forces.  Gravity and the electromagnetic force are the non-contact forces we discuss most often in this course (the strong force and the weak force are the other two non-contact forces).  Objects need not be touching for a non-contact force to affect them.

• Kinematics only described the motion of objects; dynamics explains why things move.

• Newton formulated three laws of motion which are the foundation of dynamics (and statics, too).

• Newton's first law:  An object stays in a state of constant velocity unless acted on by a force.  This means the object may move in a straight line at constant speed, or may stay at rest (a state of zero velocity).  This is the idea of inertia.  Inertia refers to the tendency of objects to persist in a state of constant velocity.  (Note: be careful with words like force, inertia, momentum, and energy that are used casually in everyday speech but have a specific meaning in physics.  Many physics students have had to overcome the belief that they "already know" what these words mean.  The upshot: they didn't know what the words mean in physics).

• If you want to think of inertia as a quantity, think of it as mass.  Changing the motion of an object with a lot of mass is difficult, so you might say it has a lot of inertia.  Note:  You would not be speaking physics.  Some physicists distinguish between gravitational mass and inertial mass.  For our purposes, we will consider them to be the same thing.  Gravitational mass is the mass as measured by the effect of a gravity field on an object.  Inertial mass is the mass as measured by the object's resistance to acceleration.

• Newton's second law relates force to acceleration.  In mathematical terms, we state it as F=ma.  That means that acceleration is the result of a force, and is directly proportional  (goes up or down as does) to the force.

• Newton's third law is stated in plain English like this:  If an object exerts a force on another object, the second object exerts a force equal in size and opposite in direction on the first object.  A physicist once said: "If you punch the wall, the wall punches you back, just as hard."  Be careful in the way you state this.  As in most physics concepts, the everyday statement of it leaves a lot to be desired in the precision department.

• When an object is in contact with a surface, the surface exerts a force perpendicular to itself on the object.  We call that force "normal force."  This is because the force is perpendicular to the surface.  Normal means perpendicular in this context.  The normal force is how we experience our weight.  If we are not in contact with a surface (falling), then we accelerate towards the center of the earth at g, and we feel weightless.

• When a force is exerted on a very strong object (say a concrete wall), it appears that the object does not move.  But how does the wall "know" to push back with an equal and opposite force?  The answer is in the molecules.  The push on the wall deforms the wall a tiny bit and stretches the molecules, which act like tiny springs.  This tension of the "tiny springs" (molecules) produces  force proportional to the push on the wall.  That is how the wall "knows" how hard to push back.  Push harder, and you stretch the molecules more.

• Static or kinetic friction occurs when the molecules of two objects in contact bond together, or "cold weld."  The amount of friction is different for different combinations of surfaces.  This is because of the different chemical composition (differences in the arrangements of the electrons and nuclei) of the two materials.  Note that a common way of naming drag is to call it air friction.  That does not mean that drag results when air cold welds with a surface.

• Cold-welding is incomplete.  It does not produce a single, "welded-together" object.  In general, this is because of the interference of dirt, oil, and oxygen in the air.  The dirt and oil are deposited on surfaces and interfere because of their presence.  The oxygen reacts with some surfaces to produce a layer of chemical on the surface that does not cold-weld very well.

• Sliding (kinetic) friction is a force that occurs when two surfaces are in contact and one is in motion relative to the other.  It opposes the direction of motion.  Note: not all frictional forces oppose the direction of motion.

• We compare the force of sliding friction between two different substances by dividing the amount of force it takes to slide an object on a surface at constant speed by the Normal force on the object.  This leads us to a dimensionless quantity we call mu, or the coefficient of friction.  The higher the mu, the more friction there is between two surfaces.  Many physics books and engineering handbooks contain tables of coefficient of friction for various combinations of substances.

• Static friction is higher than kinetic friction for a surface.  This is because left over time, the object bonds more completely to the surface.  A common experience is to slide a heavy object from rest.  Once the object is moving, the force you apply to keep it moving is less than the force to start it.

• Rolling friction is generally very low (this is the reason ball and roller bearings are used so often).  This is because any point on the wheel always contacts a different point on the surface.  The  two surfaces don't slide.  The friction results from the deformation of the surface and the wheel as the wheel moves along.

• Objects moving through the air are subject to a drag force.  When the gravitational force pulling on a falling object equals the drag force, the object moves at constant velocity.  This velocity is called terminal velocity.  The drag force is proportional to the square of the velocity of the object (and to the cross-sectional area of the object, the density of the air, and the coefficient of drag). For the exact relationship, consult a college physics book.

• The coefficient of drag is analogous to the coefficient of friction.  It is a dimensionless quantity that is a measure of how "slippery" an object is in air.

• Forces are vectors.  They follow the rules of vectors.  See the text and the vectors concepts page for more info.

• To solve dynamics problems, we follow a time-honored procedure.  First, draw a free-body diagram, depicting all the forces acting on the object being considered.  In general in this unit, most objects will be subject to a gravitational force and to a force from everything that touches them.  Second, write "sum of the forces" equations for the forces.  Be sure to only add x forces to x forces, and y forces to y forces.  Third, solve the equations for the desired quantity(ies).

• The sum of the forces is always equal to the Net Force.  This is the single "leftover" force that acts on the object in the direction under consideration.  If there is a non-zero net force, it is equal to ma (Newton's Second Law), and the object accelerates in the direction of the net force.  A non-zero net force causes acceleration.  The net acceleration is what the thing is observed to do.  If the net force is zero, the object either remains at rest or moves at constant velocity.