#Engineering Mechanics Previous Question papers two marks questions and answers

• 1 Degrees-of-freedom of a mechanical system Degree-
of-freedom of a general mechanical system is defined
as the minimum number of independent variables
required to describe its configuration completely. The
set of variables (dependent or independent) used to
describe a system are termed as the configuration
variables. For a mechanism, these can be either
Cartesian coordinates of certain points on the
mechanism, or the joint angles of the links, or a
combination of both. The set of configuration variables
form what is known as the configuration space
(denoted by C) of the mechanism.

1
• In physics, the degree of freedom (DOF) of
a mechanical system is the number of
independent parameters that define its
configuration. ... The position and orientation
of a rigid body in space is defined by three
components of translation and three
components of rotation, which means that it
has six degrees of freedom

• It is the angle between normal reaction and
frictional force ,when applied force on body
changed through 360 degree

4.Coulomb's law of friction
• The law states that for two dry solid surfaces
sliding against one another, the magnitude of
the kinetic friction exerted through the
surface is independent of the magnitude of
the velocity (i.e., the speed) of the slipping of
the surfaces against each other.

• The law states that for two dry solid surfaces sliding
against one another, the magnitude of the kinetic
friction exerted through the surface is independent of
the magnitude of the velocity (i.e., the speed) of the
slipping of the surfaces against each other.
• Note that the direction of the kinetic friction does
depend on the direction of the velocity -- it is precisely
the opposite direction.
• Coulomb's law of friction is part of the Coulomb model
of friction, a model for the behavior of frictional forces
between two dry solid surfaces in contact.

5.CENTROID
• The plane figures (like triangle, quadrilateral,
circle etc.) have only areas, but no mass.
• The centre of area of such figures is known as
centroid. The method of finding out the
centroid of a figure is the same as that of
finding out the centre of gravity of a body.
• In many books, the authors also write centre
of gravity for centroid and vice versa.

• The theorem of parallel axis states that
the moment of inertia of a body about an axis
parallel to an axis passing through the centre
of mass is equal to the sum of the moment of
inertia of body about an axis passing through
centre of mass and product of mass and
square of the distance between the two axes.

• ASSUMPTIONS FOR PROJECTILE MOTION
• The acceleration due to gravity is constant
over the range of motion and is directed
downward. The medium of projectile
motion is assumed to be non-resistive (i.e. air
resistance is negligible). The rotation of earth
does not affected the motion

Constrained Motion
• Constrained Motion. In some cases a particle is
forced to move along a curve or surface. This
curve or surface is referred to as a constraint, and
the resulting motion is called constrained motion.
The particle exerts a force on the constraint, and
by Newton’s third law the constraint exerts a
force on the particle. This force is called the
reaction force, and is described by giving its
components normal to the motion, denoted N,
and parallel to the motion, denoted f.

• 4. Periodic time. It is the time taken by a particle for one complete
oscillation. Mathematically,
• periodic time,
• T=2PIE/ ω
• where ω = Angular velocity of the particle in rad/s.
• It is thus obvious, that the periodic time of a S.H.M. is independent
of its amplitude.
• 5. Frequency. It is the number of cycles per second and is equal to
• 1/T
• where T is the periodic
• time. Frequency is generally denoted by the letter ‘n’. The unit of
frequency is hertz
• (briefly written Hz) which means frequency of one cycle per second

The center of percussion
• The center of percussion is the point on an
extended massive object attached to a pivot
where a perpendicular impact will produce no
reactive shock at the pivot. Translational and
rotational motions cancel at the pivot when
an impulsive blow is struck at the center of
percussion

Center of Percussion
• The motion (or lack of motion) of the suspension point of
an object is observed when the object is struck a blow.
• What it shows
• The center of percussion (COP) is the place on a bat or
racket where it may be struck without causing reaction at
the point of support. When a ball is hit at this spot, the
contact feels good and the ball seems to spring away with
its greatest speed and therefore this is often referred to as
the sweet spot. At points other than this spot, the bat or
racket may vibrate or even sting your hands. This
experiment shows the effect by demonstrating what
happens when you strike a suspended model of a bat at
various places.

Thank you for watching this video

What are concurrent forces,colinner
forces , coplanar forces
• 1. Coplanar forces. The forces, whose lines of
action lie on the same plane, are known as
• coplanar forces.
• 2. Collinear forces. The forces, whose lines of
action lie on the same line, are known as
• collinear forces

• 3. Concurrent forces. The forces, which meet
at one point, are known as concurrent forces.
• The concurrent forces may or may not be
collinear.

Conditions for Equilibrium.
• Conditions for Equilibrium. An object is
in equilibrium if ; The resultant force acting on
the object is zero. The sum of the moments
acting on an object must be zero.

• Laws of solid friction: The frictional force
between two surfaces opposes the relative
motion between the layers.
• Frictional force is independent of the area of
contact between the surfaces if normal
reaction is constant.
• Limiting friction is directly proportional to the
normal reaction in static friction.

angle of repose
The steepest angle at which a sloping surface
formed of loose material is stable.
• Definition of angle of repose
• 1.physics : the angle that the plane of contact
between two bodies makes with the horizontal
when the upper body is just on the point of
sliding : the angle whose tangent is the
coefficient of friction between the two bodies
• 2. angle of rest : the angle of maximum slope at
which a heap of any loose solid material (as
earth) will stand without sliding

The parallel axis theorem or Huygens
Steiner theorem

MOMENT OF INERTIA OF A PLANE
AREA

• UNITS OF MOMENT OF INERTIA
• As a matter of fact the units of moment of
inertia of a plane area depend upon the units
of
• the area and the length. e.g.,
• 1. If area is in m2 and the length is also in m,
the moment of inertia is expressed in m4.
• 2. If area in mm2 and the length is also in mm,
then moment of inertia is expressed in mm4.

• Moment of Inertia Example
• Imagine you are on a bus right now. You find a
seat and sit down. The bus starts moving
forward. After a few minutes, you arrive at a
bus stop and the bus stops. What did you
experience at this point? Yes. When the bus
stopped, your upper body moved forward
whereas your lower body did not move.

• Why is that? It is because of Inertia. Your lower body is in
contact with the bus but your upper body is not in contact
with the bus directly. Therefore, when the bus stopped,
your lower body stopped with the bus but your upper body
kept moving forward, that is, it resisted change in its state.
• Similarly, when you board a moving train, you experience a
force that pushes you backward. That is because before
boarding the train you were at rest. As soon as you board
the moving train, your lower body comes in contact with
the train but your upper body is still at rest. Therefore, it
gets pushed backward, that is, it resists change in its state.
• Understand the Theorem of Parallel and Perpendicular Axis
here in detail.

• What is Inertia?
• What is Inertia? It is the property of a body by virtue of
which it resists change in its state of rest or motion.
But what causes inertia in a body? Let’s find out.
• Inertia in a body is due to it mass. More the mass of a
body more is the inertia. For instance, it is easier to
throw a small stone farther than a heavier one.
Because the heavier one has more mass, it resists
change more, that is, it has more inertia.
•

• Moment of Inertia Definition
• So we have studied that inertia is basically mass. In
rotational motion, a body rotates about a fixed axis.
Each particle in the body moves in a circle with linear
velocity, that is, each particle moves with an angular
acceleration. Moment of inertia is the property of the
body due to which it resists angular acceleration, which
is the sum of the products of the mass of each particle
in the body with the square of its distance from the
axis of rotation.
• Formula for Moment of Inertia can be expressed as:
• ∴ Moment of inertia I = Σ miri
2

• Linear motion involves an object moving from
one point to another in a straight
line. Rotational motion involves an
object rotating about an axis. – Examples
include a merry-go-round, the rotating earth,
a spinning skater, a top, and a turning wheel.
➢What causes rotational motion?

D'Alembert's form of the principle of virtual work states
that a system of rigid bodies is in dynamic equilibrium
when the virtual work of the sum of the applied forces and
the inertial forces is zero for any virtual displacement of the
system.

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