Physical Chemistry Third Edition

622 14 Classical Mechanics and the Old Quantum Theory

In addition to the base units, there are a number of derived units. Thenewton(N) is

the SI unit of force:

1N1kgms−^2 (definition) (14.2-4)

Thepascal(Pa) is the SI unit of pressure (force per unit area):

1Pa1Nm−^2 1kgm−^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 thejoule(J):

1J1Nm1kgm^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 lawis called thelaw 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 thelaw of accelerationand is expressed by the

equation

Fmam

dv

dt

m

d^2 r

dt^2

(14.2-7)

wheretrepresents the time. In this equation the vectorFis the force acting upon an

object of massm,ris its position vector,vis its velocity, which is the rate of change

of its position, andais its acceleration, which is the rate of change of the velocity. The

xcomponent of the acceleration is

ax

dvx

dt



d^2 x

dt^2

(14.2-8)

with similar equations for theyandzcomponents. Equation (14.2-7) is equivalent to

three scalar equations.

Fxmaxm

dvx

dt

m

d^2 x

dt^2

(14.2-9a)

Fymaym

dvy

dt

m

d^2 y

dt^2

(14.2-9b)

Fzmazm

dvz

dt

m

d^2 z

dt^2

(14.2-9c)

Newton’s third lawis called thelaw of action and reaction. It asserts that ifF 21 is

the force exerted on object 2 by object 1, and ifF 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