Sir Isaac Newton and the Unification of Physics and Astronomy:

 http://csep10.phys.utk.edu/astr161/lect/history/newton.html

One way to learn about forces applied to objects, and about how vectors are calculated, is to learn to draw "free body diagrams."

If the motion in the diagram takes place on Earth, what is one force that you can be sure will be part of the free body diagram?
 
Introduction to Free Body Diagrams:

http://eta.physics.uoguelph.ca/tutorials/fbd/intro.html

 

Rolling Friction:

http://webphysics.davidson.edu/faculty/dmb/PY430/Friction/rolling.html

Newton's First Law

Newton's first law does not say what happens for an object with zero net force, that is, multiple forces that cancel; it says what happens in the absence of a force. This is a subtle but important difference that allows us to define force as that which causes a change in the motion. The description of an object under the effect of forces that balance is covered by Newton's second law.

 

Force is the Cause of Changes in Motion

Force does not cause motion. We can have motion in the absence of forces, as described in Newton's first law. Force is the cause of changes in motion, as measured by acceleration.

 

ma is Not a Force

Equation 5.2 does not say that the product ma is a force. All forces on an object are added vectorially to generate the net force on the left side of the equation. This net force is then equated to the product of the mass of the object and the acceleration that results from the net force. Do not include an "ma force" in your analysis of the forces on an object.

 

"Weight of an Object"

We are familiar with the everyday phrase, the "weight of an object." However, weight is not an inherent property of an object, but rather a measure of the gravitational force between the object and the Earth. Thus, weight is a property of a system of items-the object and the Earth.

 

Kilogram is Not a Unit of Weight

You may have seen the "conversion" 1 kg = 2.2 lb. Despite popular statements of weights expressed in kilograms, the kilogram is not a unit of weight, it is a unit of mass. The conversion statement is not an equality; it is an equivalence that is only valid on the surface of the Earth.

 

n does not Always Equal mg

We find that n = mg (the normal force has the same magnitude as the gravitational force). However, this is not generally true. If an object is on an incline, if there are applied forces with vertical components, or if there is a vertical acceleration of the system, then n mg. Always apply Newton's second law to find the relationship between n and mg.

 

Newton's Third Law

This is such an important and often misunderstood concept that it will be repeated here in a Pitfall Prevention. Newton's third law action and reaction forces act on different objects. Two forces acting on the same object, even if they are equal in magnitude and opposite in direction, cannot be an action-reaction pair.

 

Free-body Diagrams

The most important step in solving a problem using Newton's laws is to draw a proper sketch-the free-body diagram. Be sure to draw only those forces that act on the object that you are isolating. Be sure to draw all forces acting on the object, including any field forces, such as the gravitational force.

The Physics Classroom - Learn to use vectors and Newton's laws to analyze the motion of objects in two dimensions. The tutorial teaches it with riverboat problems, and the examples of projectiles or inclined planes.