1. In the MKS system of units, force has the units of newtons, N.  We can see what a newton is from Newton’s 2nd law: Force = Mass x Acceleration

2. Since mass is a scalar, and acceleration is a vector, we must have that mass x acceleration is a vector quantity. Therefore, force must be a vector quantity.  Newton’s 2nd law is therefore a statement involving vector addition, which we can perform either graphically (not what we’d prefer!) or analytically (meaning vector components!).  We thus write Newton’s 2nd law  in the more useful forms:

3. Note that a special but important case of Newton’s 1st law is the case in which v = 0 = constant.  In this case, the first law says that an object at rest  will stay at rest until it is acted upon by a net, external force. 

4. Note that Newton’s 2nd law relates particle kinematics (motion) to particle dynamics (forces). Therefore, if the acceleration is a constant (meaning the forces are constant), then we can use the kinematic equations to gain knowledge of the forces acting on the object, and vice versa.

5. If you think about it, Newton’s first law (or second law, for that matter) may not always seem to hold true.  Think, for example, about rolling a pool  ball across a pool table.  You roll it, and it rolls straight across the table with (approximately) constant speed.  Its velocity is therefore constant since there is no net external force acting on it.  You roll it again, and it rolls straight across.  You roll it yet again, but this time the ball curves across the table! What  happened?! Well, what we didn’t tell you was that the table was in the back of a big truck, which was originally traveling down a straight road with a  constant velocity. However, just as we were rolling the ball for the third time, the truck started going around a curve.  This resulted in the path followed by the ball being curved on the table top.  We say that Newton’s first law holds true in the reference frame on the ground, but not in the reference frame inside the truck (the ball was still trying to go straight — its path seemed curved in the truck because the table and truck were moving in a curved path beneath it!).  Since Newton’s first law is sometimes called the Law of Inertia,  reference frames (such as the ground) in which Newton’s first law hold true are called inertial reference frames.  Likewise, reference frames (such as the truck going around the curve) in which Newton’s  first law do not seem to hold true are called non-inertial reference frames.  In general, any reference frame which is accelerating relative to an inertial reference frame is a  non-inertial reference frame.  We will always use inertial reference frames when solving force problems in this course.