Law 1 

A body will continue in a state of rest or uniform motion unless acted on by an
external force. 

Often called the law of inertia: 

The inertia of a body is a measure of its reluctance to change the state of
its motion. 

This gives us the concept of "inertial mass". 

(Bodies having
large mass are reluctant to change... try standing in front of a moving
truck !) 



Law 2 

The net (or resultant) force acting on a body is equal to the product of its
mass and its acceleration. 

Net (resultant) force = mass × acceleration 

∑ F = ma 

click here for experimental verification of this law 



Law 3 

If body A exerts a force on body B then body B exerts an equal magnitude but
opposite sense force on body A. 



This statement reminds us that the term "a force" should always be considered
as describing an interaction between two bodies and that both the bodies
experience the same magnitude of interaction. 



This, of course, does not mean that the effect of the interaction will
be the same on the two bodies: think again about the "standing in front of a
moving truck" example above. 



In Law 2 above, the symbol ∑F means the sum of forces. 



If the forces act along the same line, as above, the arithmetic is trivial: 

If F_{1} has magnitude 4N and F_{2}
has magnitude 10N then the magnitude of ∑F (the resultant
force)
is simply given by +10 + (4) = 6N 



Remember that force is a vector quantity. 

This reminds us that this sum will often be a vector sum. 

We use bold letters to represent vectors. 



If
the two forces shown above act on a body then ∑F
means that we must do a vector addition to find the resultant of the two forces. 



If the magnitude of F_{1} is
3N and the magnitude of F_{2} is
4N, then the magnitude of their resultant
F_{R}
is 5N acting at about 48.6° to F_{2} 

click here for a reminder about vector addition 



Example: Using Newton's Second Law of Motion 

An object of mass m = 20kg
rests on a horizontal surface. 

Calculate the magnitude of the force exerted by the surface on the object in the following situations. 



a) Surface stationary or moving with
constant velocity 


Since the forces all act in the same line in this example, ∑F will represent the
simple arithmetic sum. 

∑F = ma
Newton's law 

also 

∑F = R + mg
sum of (magnitudes of) forces 

but, here a = 0 

R + mg = 0 

R = mg = 196N 

(remember g is directed in the negative sense, as defined here) 



b) Surface accelerating upwards at 2ms^{2} 




∑F = ma Newton's law 

also 

∑F = R + mg
sum of (magnitudes of) forces 

but, here a = +2ms^{2} 

R +
mg = ma so R = m(a  g) 

therefore 

R = 20(2  (9.8)) = 236N 







c) Surface accelerating downwards at 9.8ms^{2} 


∑F = ma Newton's law 



∑F = R + mg
sum of (magnitudes of) forces 

but, here a = 9.8ms^{2} 

R +
mg = ma so R = m(a  g) 

therefore 

R = 20(9.8  (9.8)) = 0N 

and, in this case, the body is said to be "weightless" 
