Chapter 3:
Kinetic Concepts for
Analyzing Human Motion
Basic Biomechanics, 6th edition
Susan J. Hall
Created by
Molly Smith
Vector Algebra
• Scalar Quantity: an undirected magnitude;
quantity is fully described by its magnitude.
– Examples: mass, volume, density, length
Vector Algebra
• Vector Quantity: a directed magnitude;
quantity that is represented by an arrow.
Arrow has an arrowhead (direction) and
length (magnitude.
– Kinetic vector quantities : force, weight,
pressure, specific weight & torque
– Kinematic vector quantities: displacement,
velocity & acceleration
Vector Composition
The composition of vectors with the same
direction requires adding their magnitudes.
Vector Composition
The composition of vectors with the opposite
directions requires subtracting their magnitudes
Vector Composition
• Resultant vector
• “Tip-to-tail” vector composition
Resultant vector
Vector #2
Vector #1
Vector Composition
The tip-to-tail method of vector composition.
Vector Composition
• Sum of three original
vectors: R=A + B + C
• Vector B starts at the
end of vector A and
vector C starts at the
end of vector B
• Resultant begins at
tail of A and ends at
head of C (-1, -6).
Vector Composition
• Sum of same three
original vectors:
R=B + A + C.
• R always starts at
the beginning of the
first vector and
terminates at the
end of the last
vector (-1, -6).
Vector Composition
• Sum of same three
original vectors:
R=C + B + A.
• Note that in each
case, regardless of
order, R has the
same rectangular
form (-1, -6 ).
Vector Resolution
• What is vector resolution?
–Operation that replaces a single
vector with two perpendicular
vectors such that the vector
composition of the two
perpendicular vectors yields the
original vector.
Vector Resolution
Vectors may be resolved into
perpendicular components. The vector
composition of each pair of components
yields the original vector.
Vector Resolution
Example: A ball is thrown into the air
Vertical
Horizontal
Graphic Solution of
Vector Problems
• Graphic vector manipulation may yield
approximate result
1 cm = 10 N
30 N = 3 cm
35 N = 4.5 cm
Trigonometric Solution of
Vector Problems
• A more accurate procedure for
quantitatively dealing with vector
problems
hypotenuse
opposite
adjacent
Trigonometric Vector
Resolution
Two rectangular components
• One directed negative x-axis (adjacent to angle)
• One directed positive y-axis (opposite to angle)
Summary
• This chapter introduced basic concepts related
to kinetics
• Vectors quantities have magnitude & direction
• Vector problems may be solved by a graphic or
a trigonometric approach.