Lecture notes of Chapter 13 of Engineering Applied Mathematics, ISBN: 9780857766151
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Course
MATH142
Institution
University Of KwaZulu-Natal (UKZN)
Book
Engineering Applied Mathematics
Dynamics is concerned with bodies that have accelerated motion. Kinematics is a study of the geometry of the motion. Kinetics is a study of the forces that cause the motion. Rectilinear kinematics refers to straight-line motion.
Lecture 11
Introduction & Rectilinear Kinematics:
Mechanics: The study of how bodies
react to forces acting on them.
Dynamics:
Statics: The study of 1. Kinematics – concerned with
bodies in equilibrium. the geometric aspects of motion
without any reference to the cause of
motion.
2. Kinetics - concerned with the
forces causing the motion
Vectors: are quantities which are fully described by both a magnitude and a direction.
eg: displacement , velocity , force ,acceleration etc.,
Scalars: are quantities which are fully described by a magnitude alone.
eg : distance , mass ,time ,volume etc 1
Linear motion: when a body moves either in a straight line or along a curved
path, then we say that it is executing linear motion.
1. when a body moves in a straight line then the linear motion is called
rectilinear motion.
eg ., an athlete running a 100 meter race along a straight track is said to be a
linear motion or rectilinear motion .
2. when a body moves along a curved in two or three dimensions path then the
linear motion is called cur vilinear motion.
eg., the earth revolving around the sun.
Rotatory motion: A body is said to be in rotatory motion when it stays at one
place and turns round and round about an axis.
example: a rotating fan, a rotating pulley about its axis.
Oscillatory motion: a body is said to be in oscillatory motion when it swings to
and fro about a mean position.
example: the pendulum of a clock, the swing etc.,
2
,What is motion? Lecture 11
when a body is continuously changing its position with respect to the surroundings,
then we say that the body is in motion.
Motion in Relative:
When we discuss the motion of something, we describe motion relative to something
else.
When sitting on a chair, your speed is zero relative to the Earth but 30 km/s relative
to the sun
when we discuss the speeds of things in our environment we mean relative to the
surface of the Earth.
Rectilinear Kinematics: Continuous Motion
A particle travels along a straight-line path defined by the
coordinate axis ( x ).
The motion of a par ticle is known if the position (location)
coordinate for particle is known for every value of time ( t ).
Position coor dinate of a par ticle is defined by positive or
negative distance of particle from a fixed or igin on the line.
Motion of the par ticle may be expressed in the form of a
function, e.g.,
Distance and Displacement
In the picture, the car moves from (point A
to point B). So it changes its position during a
time interval ( t ).
Distance: refers to how far an object travels.
This is a scalar quantity. For example: the car
traveled (35 km).
We are only concerned with the length of
travel we don’t distinguish between directions.
Distance = dx + dy = 4 + 3 = 7 km
Displacement: refers to how far the object
travels, but also adds direction. This is a vector
quantity. For example: the car traveled (35km
36.8o
to the east).
Speed:
Speed is a measure of how fast something moves.
Speed is a scalar quantity, specified only by its magnitude.
Speed is defined as the distance covered per unit time:
speed = distance / time = x / t ( m/s, km/h, foot/min, … etc ) 4
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