Understanding the concepts of inertia, mass, weight, pressure,
volume, density, specific weight, torque, and impulse provides a
useful foundation for understanding the effects of forces.
In common usage, inertia means
resistance to action or to change (Figure 3-1). Similarly, the mechanical
definition is resistance to acceleration. Inertia is the tendency
of a body to maintain its current state of motion, whether motionless
or moving with a constant velocity. For example, a 150 kg weight
bar lying motionless on the floor has a tendency to remain motionless.
A skater gliding on a smooth surface of ice has a tendency to continue
gliding in a straight line with a constant speed.
A static object tends to maintain its motionless state
because of inertia.
Although inertia has no units of measurement, the amount of inertia
a body possesses is directly proportional to its mass. The more
massive an object is, the more it tends to maintain its current state
of motion and the more difficult it is to disrupt that state.
A skater has a tendency to continue gliding
with constant speed and direction due to inertia.
Mass (m) is the quantity of matter
composing a body. The common unit of mass in the metric system is the
kilogram (kg), with the English unit of mass being the slug, which is much larger than a
A force (F) can be thought of as
a push or a pull acting on a body. Each force is characterized by
its magnitude, direction, and point of application to a given body.
Body weight, friction, and air or water resistance are all forces
that commonly act on the human body. The action of a force causes
a body’s mass to accelerate:
Units of force are units of mass multiplied by units of acceleration
(a). In the metric system, the most common unit of force is the
Newton (N), which is the amount of force required to accelerate 1
kg of mass at 1 m/s2:
In the English system, the most common unit of force is the pound
(lb). A pound of force is the amount of force necessary to accelerate
a mass of 1 slug at 1 ft/s2, and 1 lb is equal
to 4.45 N:
Because a number of forces act simultaneously in most situations,
constructing a free body diagram is
usually the first step when analyzing the effects of forces on a
body or system of interest. A free body is
any object, body, or body part that is being focused upon for analysis.
A free body diagram consists of a sketch of the system being analyzed
and vector representations of the acting forces (Figure 3-2). Even
though a hand must be applying force to a tennis racket in order
for the racket to forcefully contact a ball, if the racket is the
free body of interest, the hand is represented in the free body
diagram of the racket only as a force vector. Similarly, if the
tennis ball constitutes the free body being studied, the force of
the racket acting on the ball is displayed as a vector.
Two free body diagrams showing the acting forces.
Since a force rarely acts in isolation, it is important to recognize
that the overall effect of many forces acting on a system or free
body is a function of the net force,
which is the vector sum of all of the acting forces. When all acting
forces are balanced, or cancel each other out, the net force is
zero, and the body remains in its original state of motion, either motionless
or moving with a constant velocity. When a net force is present,
the body moves in the direction of the net force and with an acceleration
that is proportional to the magnitude of the net force.
A body’s center of gravity,
or center of mass, is the point around which the body’s
weight is equally balanced, no matter how the body is positioned,
(see Chapter 13). In motion analyses, the motion of the center of
gravity serves as an index of total body motion. From a kinetic
perspective, the location of the center of mass determines the way
in which the body responds to external forces.
Weight is defined as the amount
of gravitational force exerted on a body. Algebraically, its definition
is a modification of the general definition of a force, with weight
(wt) being equal to mass (m) multiplied by the acceleration of gravity
Since weight is a force, units of weight are units of force—either
N or lb.
As the mass of a body increases, its weight increases proportionally.
The factor of proportionality is the acceleration of gravity, which
is −9.81 m/s2. The negative sign
indicates that the acceleration of gravity is directed downward,
or toward the center of the earth. On the moon or another planet
with a different gravitational acceleration, a body’s weight
would be different, although its mass would remain the same.
Because weight is a force, it is also characterized by magnitude,
direction, and point of application. The direction in which weight
acts is always toward the center of the earth. Because the point
at which weight is assumed to act on a body is the body’s
center of gravity, the center of gravity is the point where the
weight vector is shown to act in free body diagrams.
Although body weights are often reported in kilograms, the kilogram
is actually a unit of mass. To be technically correct, weights should
be identified in Newtons and masses reported in kilograms. Sample
Problem 3.1 illustrates the relationship between mass and weight.
Although a body’s mass remains
unchanged on the moon, its weight is less due to smaller gravitational
acceleration. Photo courtesy of NASA.
1. If a scale shows that an individual has a mass
of 68 kg, what is that individual’s weight?
(Mass may be multiplied by the acceleration of gravity to convert
to weight within either the English or the metric system.)
Mass in kg may be multiplied by the conversion factor 2.2 lb/kg
to convert to weight in pounds:
2. What is the mass of an object weighing 1200 N?
(Weight may be divided by the acceleration of gravity within
a given system of measurement to convert to mass.)
Pressure (p) is defined as force
(F) distributed over a given area (A):
Units of pressure are units of force divided by units of area.
Common units of pressure in the metric system are N per square centimeter
(N/cm2) and Pascals (Pa). One Pascal represents
one Newton per square meter (Pa = N/m2).
In the English system, the most common unit of pressure is pounds
per square inch (psi or lb/in2).
The pressure exerted by the sole of a shoe on the floor beneath
it is the body weight resting on the shoe divided by the surface
area between the sole of the shoe and the floor. As illustrated
in Sample Problem 3.2, the smaller amount of surface area on the
bottom of a spike heel as compared to a flat sole results in a much
larger amount of pressure being exerted.
Is it better to be stepped on by a woman wearing a spike heel
or by the same woman wearing a smooth-soled court shoe? If a woman’s
weight is 556 N, the surface area of the spike heel is 4 cm2,
and the surface area of the court shoe is 175 cm2, how
much pressure is exerted by each shoe?
Wanted: pressure exerted by the spike heel
pressure exerted by the court shoe
Deduction: It is necessary to recall that weight is a force.
Comparison of the amounts of pressure exerted by the two shoes:
Therefore, 43.75 times more pressure is exerted by the spike
heel than by the court shoe worn by the same woman.
A body’s volume is the
amount of space that it occupies. Because space is considered to
have three dimensions (width, height, depth), a unit of volume is
a unit of length multiplied by a unit of length multiplied by a
unit of length. In mathematical shorthand, this is a unit of length
raised to the exponential power of three, or a unit of length cubed. In the metric system, common
units of volume are cubic centimeters (cm3), cubic meters
(m3), and liters (l):
In the English system of measurement, common units of volume
are cubic inches (in3) and cubic feet (ft3). Another
unit of volume in the English system is the quart (qt):
Volume should not be confused with weight or mass. An 8 kg shot
and a softball occupy approximately the same volume of space, but
the weight of the shot is much greater than that of the softball.
Pairs of balls that are similar in volume
but markedly different in weight.
The concept of density combines
the mass of a body with the body volume. Density is defined as mass
per unit of volume. The conventional symbol for density is the Greek
letter rho (ρ).
Units of density are units of mass divided by units of volume.
In the metric system, a common unit of density is the kilogram per
cubic meter (kg/m3). In the English system of
measurement, units of density are not commonly used. Instead, units
of specific weight (weight density) are employed.
Specific weight is defined as weight
per unit of volume. Because weight is proportional to mass, specific
weight is proportional to density. Units of specific weight are
units of weight divided by units of volume. The metric unit for
specific weight is Newtons per cubic meter (N/m3),
and the English system uses pounds per cubic foot (lb/ft3).
Although a golf ball and a ping-pong ball occupy approximately
the same volume, the golf ball has a greater density and specific
weight than the ping-pong ball because the golf ball has more mass
and more weight. Similarly, a lean person with the same body volume
as an obese person has a higher total body density because muscle
is denser than fat. Thus, percent body fat is inversely related
to body density.
When a force is applied to an object such as a pencil lying on
a desk, either translation or general motion may result. If the
applied force is directed parallel to the desktop and through the
center of the pencil (a centric force),
the pencil will be translated in the direction of the applied force.
If the force is applied parallel to the desktop but directed through
a point other than the center of the pencil (an eccentric
force), the pencil will undergo both translation and rotation
A. Centric forces produce
translation. B. Eccentric forces produce
translation and rotation.
The rotary effect created by an eccentricforce is known as torque (T), or moment of force. Torque,
which may be thought of as rotaryforce, is the angular equivalent of
linear force. Algebraically, torque is the product of force (F)
and the perpendicular distance (d⊥) from the force’s
line of action to the axis of rotation:
The greater the amount of torque acting at the axis of rotation,
the greater the tendency for rotation to occur. Units of torque
in both the metric and the English systems follow the algebraic
definition. They are units of force multiplied by units of distance:
Newton-meters (N-m) or foot-pounds (ft-lb).
When a force is applied to a body, the resulting motion of the
body is dependent not only on the magnitude of the applied force
but also on the duration of force application. The product of force (F)
and time (t) is known as impulse:
A large change in an object’s state of motion may result
from a small force acting for a relatively long time or from a large
force acting for a relatively short time. A golf ball rolling across
a green gradually loses speed because of the small force of rolling
friction. The speed of a baseball struck vigorously by a bat changes
because of the large force exerted by the bat during the fraction
of a second it is in contact with the ball. When a vertical jump
is executed, the larger the impulse generated against the floor,
the greater the jumper’s takeoff velocity and the higher
the resulting jump.
Units of physical quantities commonly used in biomechanics are
shown in Table 3-1.
Table 3-1 Common Units for Kinetic Quantities ||Download (.pdf)
Table 3-1 Common Units for Kinetic Quantities
|Quantity||Symbol||Metric Unit||English Unit|
|Volume (solids)(liquids)||V||m3 liter||ft3 gallon|
|Impulse||N • s||lb • s|