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

• 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.

(Lab)
• 1 st 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

nd
•
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

• 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
.
The Vector
Sum of All

Forces Acting on Mass m!
∑F = ma

• Newton’s 2nd Law
:
∑F = ma
Based on experiment!
Not derivable mathematically!!
A VECTOR equation!! Holds component by component.
∑F x
= ma x
, ∑F y
= ma y
, ∑F z
= ma z
ONE OF THE MOST
FUNDAMENTAL & IMPORTANT
LAWS OF CLASSICAL PHYSICS!!!

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

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
F
1
& F
2 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 2 nd Law equations x & y directions.
5.
Use Newton’s 2 nd Law equations & algebra to solve for unknowns in the problem. x & y directions.

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

rd
•
2 nd 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 3 rd Law : “Whenever one object exerts a force an
F
12 on a second object, the second object exerts equal and opposite force -F
12 on the first object.”
– Law of Action-Reaction : “Every action has an equal & opposite reaction”.
(Action-reaction forces act on DIFFERENT objects!)

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

rd

Action-Reaction Pairs: On Different Bodies