#Engineering Mechanics Previous Question papers two marks questions and answers

#Engineering mechanics Previous Question papers two marks questions and answers according #JNTUA Syllabus

2. •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.

3. 1
•In physics, thedegree of freedom(DOF) of
amechanicalsystem 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 sixdegrees of freedom

4. 2.Lami’s theorem

5. 3.CONE OF FRICTION

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

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

8. •The law states that for two dry solid surfaces sliding
against one another, the magnitude of thekinetic
frictionexerted 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 thedirectionof the kinetic friction does
depend on thedirectionof the velocity --it is precisely
the opposite direction.
•Coulomb's law of friction is part of theCoulomb model
of friction, a model for the behaviorof frictional forces
between two dry solid surfaces in contact.

9. 5.CENTROID
•Theplanefigures(liketriangle,quadrilateral,
circleetc.)haveonlyareas,butnomass.
•Thecentreofareaofsuchfiguresisknownas
centroid.Themethodoffindingoutthe
centroidofafigureisthesameasthatof
findingoutthecentreofgravityofabody.
•In many books, the authors also write centre
of gravity for centroid and vice versa.

11. •Thetheoremofparallelaxisstatesthat
themomentofinertiaofabodyaboutanaxis
paralleltoanaxispassingthroughthecentre
ofmassisequaltothesumofthemomentof
inertiaofbodyaboutanaxispassingthrough
centreofmassandproductofmassand
squareofthedistancebetweenthetwoaxes.

13. •ASSUMPTIONSFORPROJECTILE MOTION
•The acceleration due to gravity is constant
over the range ofmotionand is directed
downward. The medium ofprojectile
motionis assumed to be non-resistive (i.e. air
resistance is negligible). The rotation of earth
does not affected themotion

14. 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.

15. •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

16. The centerof percussion
•The centerof 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 centerof
percussion

17. Centerof 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 centerof 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.

18. Thank you for watching this video

20. 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

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

22. ConditionsforEquilibrium.
•ConditionsforEquilibrium. An object is
inequilibriumif ; The resultant force acting on
the object is zero. The sum of the moments
acting on an object must be zero.

26. Laws of Solid friction

27. •Lawsofsolidfriction:Thefrictionalforce
betweentwosurfacesopposestherelative
motionbetweenthelayers.
•Frictionalforceisindependentoftheareaof
contactbetweenthesurfacesifnormal
reactionisconstant.
•Limitingfrictionisdirectlyproportionaltothe
normalreactioninstaticfriction.

28. angle of repose
The steepest angle at which a sloping surface
formed of loose material is stable.
•Definition ofangle 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

29. Theparallel axis theoremorHuygens
Steiner theorem

31. MOMENT OF INERTIA OF A PLANE
AREA

32. •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 mm2and the length is also in mm,
then moment of inertia is expressed in mm4.

33. •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.

34. •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 theTheorem of Parallel and Perpendicular Axis
herein detail.

35. •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.
•

36. •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 inertiais the property of the
body due to which it resists angular acceleration, which
is the sum of the products of themass 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 m
ir
i
2

37. •Linear motioninvolves an object moving from
one point to anotherina straight
line.Rotational motioninvolves an
objectrotatingabout an axis. –Examples
include a merry-go-round, therotatingearth,
a spinning skater, a top, and a turning wheel.
➢What causesrotational motion?

42. D'Alembert'sform of theprincipleof 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.