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King Fahd University of
Petroleum & Minerals
Mechanical Engineering
Dynamics ME 201
BY
Dr. Meyassar N. Al-Haddad
Lecture # 10
Sir Isaac Newton
1642-1727
Proposed fundamental
laws that are the basis
of modern mechanics
3 laws of motion
law of gravitation
First law
• Law of inertia - a body in motion will stay in
motion and a body at rest will stay at rest unless
acted upon by a net external force.
• A particle originally at rest, or moving in a straight
line with a constant velocity, will remain in this
state provided the particle is not subjected to an
unbalance force.
• Static law
Second law
• A particle acted upon by an unbalanced force F
experiences an acceleration that has the same
direction as the force and a magnitude that is
directly proportional to the force
F a
F ma
a1
a2
F1
F2
F3
Third law
• Law of action-reaction - for every action, there is
an equal and opposite reaction
• The mutual forces of action and reaction
between two particles are equal, opposite,
and collinear.
• Fb,a= -Fa,b
Newton's Law of Universal
Gravitation
• Law of gravitation - all bodies are attracted to one
another with a force proportional to the product of
their masses and inversely proportional to the
square of the distance between them.
–
–
–
–
m1m2
F G 2
r
F = forces of attraction
G = universal constant of gravitation = 66.73(10-12)m3/(kg.s2)
m1,m2 = mass of each of the two particle
r = distance between the centers of the two particles
Gravity on earth?
Newton's Law of Universal Gravitation
Compare with F = mg so g = GM/r2
Mm
F G 2
r
• g depends inversely on the square of the distance
• g depends on the mass of the planet
• Nominally, g = 9.81 m/s2 or 32.2 ft/s2
– At the equator
g = 9.78 m/s2
– At the North pole g = 9.83 m/s2
– g on the Moon is 1/6 of g on Earth.
Mass and Weight
• Weight
– the amount of gravitational force
exerted on a body
•F = m g
• W= m g
– W: weight (units: N or lbs)
– m: mass of the body (units: kg)
– g: gravitational acceleration (9.81 m/s2,
32.2 ft/s2)
• As the mass of a body increases, its’
weight increases proportionally
13.2 The Equation of Motion
Free Body and Kinetic Diagram
 F  ma
• Free-Body diagram
• Kinetic diagram
13.3 Equation of Motion for a System of
Particles
 F  ma
Fi  f i  mi a i
 F  ma
G