1. Newton’s First Law Mathematical Statement of Newton’s 1st Law:
If v = constant, ∑F = 0 OR if v ≠ constant, ∑F ≠ 0

2. Mass (Inertia)
Inertia  The tendency of a body to maintain its state of rest or motion.
MASS: Property of an object that specifies how much resistance an object exhibits to changes in it’s velocity.
A measure of the inertia of a body
Quantity of matter in a body
A scalar quantity
Quantify mass by having a standard mass = Standard Kilogram (kg) (Similar to standards for length & time).
SI Unit of Mass = Kilogram (kg)
cgs unit = gram (g) = 10-3 kg
Weight: (NOT the same as mass!) The force of gravity on an object.

3. Newton’s Second Law (Lab)
1st Law: If no net force acts, object remains at rest or in uniform motion in straight line.
What if a net force acts? Do Experiments.
Find, if the net force ∑F  0  The velocity v changes (in magnitude or direction or both).
A change in the velocity v (dv)
 There is an acceleration a = (dv/dt) OR
A net force acting on an object produces an acceleration! ∑F  0  a

4. Newton’s 2nd Law
Experiment: The net force ∑F on an object & the acceleration a of that object are related.
HOW? Answer by EXPERIMENTS!
Thousands of experiments over hundreds of years find (object of mass m) :
a  (∑F)/m (proportionality)
Choose the units of force so that this is not just a proportionality but an equation:
a  (∑F)/m
OR: (total force!)  ∑F = ma

5. ∑F = ma Newton’s 2nd Law: ∑F = ma
∑F = the net (TOTAL!) force acting on mass m
m = the mass (inertia) of the object.
a = acceleration of the object. Description of the
effect of ∑F. ∑F is the cause of a.
∑F = ma
The Vector
Sum of All 
Forces Acting
on Mass m!

6. FUNDAMENTAL & IMPORTANT LAWS OF CLASSICAL PHYSICS!!!
Based on experiment!
Not derivable
mathematically!!
Newton’s 2nd Law:
∑F = ma
A VECTOR equation!! Holds
component by component.
∑Fx = max, ∑Fy = may, ∑Fz = maz
ONE OF THE MOST
FUNDAMENTAL & IMPORTANT
LAWS OF CLASSICAL PHYSICS!!!

7. 2nd Law Force = an action capable of accelerating an object.
Units of force: SI unit = the Newton (N)
∑F = ma , units = kg m/s2  1N = 1 kg m/s2

8. Example 5.1: Accelerating Hockey Puck
See Figure: A hockey puck, mass
m = 0.3 kg, slides on the horizontal,
frictionless surface of an ice rink.
 Two hockey sticks strike the puck
simultaneously, exerting forces
F1 & F2 on it. Calculate the
magnitude & direction of the
acceleration.
Steps to Solve the Problem
1. Sketch the force diagram (“Free Body Diagram”).
2. Choose a coordinate system.
3. Resolve Forces (find components) along x & y axes.
4. Write Newton’s 2nd Law equations x & y directions.
5. Use Newton’s 2nd Law equations & algebra to solve for unknowns in the problem. x & y directions.

9. Example

10. Sect. 5.5: Gravitational Force & Weight
Weight  Force of gravity on an object.
Varies (slightly) from location to location because g varies.
Write as Fg  mg. (Read discussion of difference between inertial mass & gravitational mass).
Consider an object in free fall. Newton’s 2nd Law:
∑F = ma
If no other forces are acting, only Fg  mg acts
(in vertical direction) ∑Fy = may or
Fg = mg (down, of course)
SI Units: Newtons (just like any force!).
g = 9.8 m/s2  If m = 1 kg, Fg = 9.8 N

11. Newton’s 3rd Law
2nd Law: A quantitative description of how forces affect motion.
BUT: Where do forces come from?
EXPERIMENTS Find: Forces applied to an object are ALWAYS applied by another object.
 Newton’s 3rd Law: “Whenever one object exerts a force F12 on a second object, the second object exerts an equal and opposite force -F12 on the first object.”
Law of Action-Reaction: “Every action has an equal & opposite reaction”. (Action-reaction forces act on DIFFERENT objects!)

12. Another Statement of Newton’s 3rd Law
“If two objects interact,
the force F12 exerted
by object 1 on object 2
is equal in magnitude
& opposite in direction
to the force F21 exerted
by object 2 on object 1.”
As in figure

13. Example: Newton’s 3rd Law

14. Action-Reaction Pairs: On Different Bodies