622
14 Classical Mechanics and the Old Quantum Theory
In addition to the base units, there are a number of derived units. The newton (N) is
the SI unit of force:
1 N 1 kg m s
−2 (definition)
(14.2-4)
The pascal (Pa) is the SI unit of pressure (force per unit area):
1 Pa 1 N m
−2
1 kg m
−1 s
−2 (definition)
(14.2-5)
The pascal is named for Blaise Pascal,
1623–1662, a famous French
philosopher, theologian, and
mathematician.
The SI unit of energy is the joule (J):
1 J 1 N m 1 kg m
2 s
−2 (definition)
(14.2-6)
The joule is named for James Prescott
Joule, 1818–1889, a great English
physicist who pioneered in the study of
thermodynamics while managing his
family’s brewery.
Newton’s Laws of Motion
According to classical mechanics the motions of particles are governed by Newton’s
three laws, which we accept as summaries and generalizations of experimental fact.
Newton’s first law is called the law of inertia: A stationary particle tends to remain
stationary unless acted on by a force, and a moving particle tends to continue moving
with unchanged velocity unless acted on by a force. The first law is a special case of
Newton’s second law, which is called the law of acceleration and is expressed by the
equation
F ma m
dv
dt
m
d 2 r
dt 2
(14.2-7)
where t represents the time. In this equation the vector F is the force acting upon an
object of mass m, r is its position vector, v is its velocity, which is the rate of change
of its position, and a is its acceleration, which is the rate of change of the velocity. The
x component of the acceleration is
a x
dv x
dt
d 2 x
dt 2
(14.2-8)
with similar equations for the y and z components. Equation (14.2-7) is equivalent to
three scalar equations.
F x ma x m
dv x
dt
m
d 2 x
dt 2
(14.2-9a)
F y ma y m
dv y
dt
m
d 2 y
dt 2
(14.2-9b)
F z ma z m
dv z
dt
m
d 2 z
dt 2
(14.2-9c)
Newton’s third law is called the law of action and reaction. It asserts that if F 21 is
the force exerted on object 2 by object 1, and if F 12 is the force exerted on object 1 by
object 2, then
F 21 −F 12 (Newton’s third law)
(14.2-10)
We tend to take Newton’s third law for granted, but if you stop and think for a moment,
it is quite interesting. If you stand on a floor and jump into the air, you put a force
14 Classical Mechanics and the Old Quantum Theory
In addition to the base units, there are a number of derived units. The newton (N) is
the SI unit of force:
1 N 1 kg m s
−2 (definition)
(14.2-4)
The pascal (Pa) is the SI unit of pressure (force per unit area):
1 Pa 1 N m
−2
1 kg m
−1 s
−2 (definition)
(14.2-5)
The pascal is named for Blaise Pascal,
1623–1662, a famous French
philosopher, theologian, and
mathematician.
The SI unit of energy is the joule (J):
1 J 1 N m 1 kg m
2 s
−2 (definition)
(14.2-6)
The joule is named for James Prescott
Joule, 1818–1889, a great English
physicist who pioneered in the study of
thermodynamics while managing his
family’s brewery.
Newton’s Laws of Motion
According to classical mechanics the motions of particles are governed by Newton’s
three laws, which we accept as summaries and generalizations of experimental fact.
Newton’s first law is called the law of inertia: A stationary particle tends to remain
stationary unless acted on by a force, and a moving particle tends to continue moving
with unchanged velocity unless acted on by a force. The first law is a special case of
Newton’s second law, which is called the law of acceleration and is expressed by the
equation
F ma m
dv
dt
m
d 2 r
dt 2
(14.2-7)
where t represents the time. In this equation the vector F is the force acting upon an
object of mass m, r is its position vector, v is its velocity, which is the rate of change
of its position, and a is its acceleration, which is the rate of change of the velocity. The
x component of the acceleration is
a x
dv x
dt
d 2 x
dt 2
(14.2-8)
with similar equations for the y and z components. Equation (14.2-7) is equivalent to
three scalar equations.
F x ma x m
dv x
dt
m
d 2 x
dt 2
(14.2-9a)
F y ma y m
dv y
dt
m
d 2 y
dt 2
(14.2-9b)
F z ma z m
dv z
dt
m
d 2 z
dt 2
(14.2-9c)
Newton’s third law is called the law of action and reaction. It asserts that if F 21 is
the force exerted on object 2 by object 1, and if F 12 is the force exerted on object 1 by
object 2, then
F 21 −F 12 (Newton’s third law)
(14.2-10)
We tend to take Newton’s third law for granted, but if you stop and think for a moment,
it is quite interesting. If you stand on a floor and jump into the air, you put a force