Object Required
Rigid-body Mechanics
Principle
Statics: deals with equilibrium of bodies under action of forces (bodies may be either at rest or move with a constant velocity).
Theory
Rigid-body Mechanics
•
Dynamics: deals with motion of bodies
(accelerated motion)
Mechanics: Fundamental Concepts
Length (Space): needed to locate position of a point in space, &
describe size of the physical system
Distances, Geometric
Properties
Time: measure of succession of events
basic quantity in
Dynamics
Mass: quantity of matter in a body
measure of inertia of a
body (its resistance to change in velocity)
Force: represents the action of one body on another
characterized by its magnitude, direction of its action, and its
point of application
Force is a Vector quantity.
Mechanics: Fundamental Concepts
Newtonian Mechanics
Length,
Time, and Mass are absolute concepts
independent of each other
Force is a derived concept
not independent of the other fundamental concepts.
Force acting on a body is related to the mass of the body
and the variation of its velocity with time.
Force can also occur between bodies that are physically
separated (Ex: gravitational, electrical, and magnetic forces)
Mechanics: Fundamental Concepts
Remember:
• Mass is a property of matter that does not
change from one location to another.
• Weight refers to the gravitational attraction of
the earth on a body or quantity of mass. Its
magnitude depends upon the elevation at
which the mass is located
• Weight of a body is the gravitational force acting on it.
Mechanics: Idealizations
To simplify application of the theory
Particle: A body with mass but with dimensions
that can be neglected
Size of earth is insignificant
compared to the size of its
orbit. Earth can be modeled
as a particle when studying its
orbital motion
Mechanics: Idealizations
Rigid Body: A combination of large number of particles in
which all particles remain at a fixed distance (practically)
from one another before and after applying a load.
Material properties of a rigid body are not required to be
considered when analyzing the forces acting on the
body.
In most cases, actual deformations occurring in structures,
machines, mechanisms, etc. are relatively small, and rigid
body assumption is suitable for analysis
Mechanics: Idealizations
Concentrated Force: Effect of a loading which is
assumed to act at a point (CG) on a body.
• Provided the area over which the load is applied
is very small compared to the overall size of the
body.
Ex: Contact Force
between a wheel
and ground.
40 kN 160 kN
Mechanics: Newton’s Three Laws of Motion
First Law: A particle originally at rest, or moving in a straight line
with constant velocity, tends to remain in this state provided the
particle is not subjected to an unbalanced force.
First law contains the principle of
the equilibrium of forces main
topic of concern in Statics
Basis of formulation of rigid body mechanics.
Mechanics: Newton’s Three Laws of Motion
Second Law: A particle of mass “m†acted upon by an
unbalanced force “F†experiences an acceleration “a†that
has the same direction as the force and a magnitude that is
directly proportional to the force.
m F = ma
Second Law forms the basis for most of
the analysis in Dynamics
Mechanics: Newton’s Three Laws of Motion
Third law is basic to our understanding of Force Forces always
occur in pairs of equal and opposite forces.
Third Law: The mutual forces of action and reaction between
two particles are equal, opposite, and collinear.
Mechanics: Newton’s Law of Gravitational Attraction
Conclusion
F = mutual force of attraction between two particles G = universal constant of gravitation Experiments G = 6.673x10-11 m3/(kg.s2) Rotation of Earth is not taken into account m1, m2 = masses of two particles r = distance between two particles 2 1 2 r m m F = G Weight of a body (gravitational force acting on a body) is required to be computed in Statics as well as Dynamics. This law governs the gravitational attraction between any two particles. Gravitational Attraction of the Earth 2 r mM W G e = W = mg Weight of a Body: If a particle is located at or near the surface of the earth, the only significant gravitational force is that between the earth and the particle Let g = G Me /r 2 = acceleration due to gravity 
Published Date
05 Mar, 2018
