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Chapter 2 Newton’s Second Law
The First Law of Thermodynamics The fundamental equation of classical mechanics is Newton’s second law of motion:

F ma (2.1)*
where m is the mass of a body, F is the vector sum of all forces acting on it at some
instant of time, and a is the acceleration the body undergoes at that instant. F and a
are vectors, as indicated by the boldface type. Vectors have both magnitude and di-
rection. Scalars (for example, m) have only a magnitude. To define acceleration, we
set up a coordinate system with three mutually perpendicular axes x, y, and z. Let r be
the vector from the coordinate origin to the particle (Fig. 2.1). The particle’s velocity v
is the instantaneous rate of change of its position vector r with respect to time:
v dr>dt (2.2)*
The magnitude (length) of the vector v is the particle’s speed v. The particle’s accel-
Figure 2.1 eration a is the instantaneous rate of change of its velocity:
2
The displacement vector r from a dv>dt d r>dt 2 (2.3)*
the origin to a particle.
A vector in three-dimensional space has three components, one along each of the
coordinate axes. Equality of vectors means equality of their corresponding compo-
nents, so a vector equation is equivalent to three scalar equations. Thus Newton’s sec-
ond law F ma is equivalent to the three equations
F ma , F ma , F ma z (2.4)
y
x
y
z
x
where F and a are the x components of the force and the acceleration. The x compo-
x x
nent of the position vector r is simply x, the value of the particle’s x coordinate.
2
2
Therefore (2.3) gives a d x/dt , and (2.4) becomes
x
2
2
2
d x d y d z
F m 2 , F m 2 , F m 2 (2.5)
y
z
x
dt dt dt
The weight W of a body is the gravitational force exerted on it by the earth. If g is
the acceleration due to gravity, Newton’s second law gives
W mg (2.6)
Units
In 1960 the General Conference on Weights and Measures recommended a single sys-
tem of units for use in science. This system is called the International System of
Units (Système International d’Unités), abbreviated SI. In mechanics, the SI uses me-
ters (m) for length, kilograms (kg) for mass, and seconds (s) for time. A force that pro-
2
duces an acceleration of one meter per second when applied to a one-kilogram mass
is defined as one newton (N):
1 N 1 kg m/s 2 (2.7)
If one were to adhere to SI units, pressures would always be given in
2
newtons/meter (pascals). However, it seems clear that many scientists will continue
to use such units as atmospheres and torrs for many years to come. The current scien-
tific literature increasingly uses SI units, but since many non-SI units continue to be
used, it is helpful to be familiar with both SI units and commonly used non-SI units.
3
SI units for some quantities introduced previously are cubic meters (m ) for volume,
3
kg/m for density, pascals for pressure, kelvins for temperature, moles for amount of
substance, and kg/mol for molar mass.