Applied Physics
Lecture 1
9/24/2024
AIG1312 Applied Physics
Course Information
Instructor :
Umar Maqbool
umar.maqbool@cust.edu.pk
Office Hours:
Monday (09:00 – 12:00)
Thursday (10:00 – 13:00)
Text Book:
Fundamentals of Physics 9th edition by: Halliday,
Resnick and Walker
Reference Books:
1. Basic Physics 2nd edition by: Karl F. Kuhn
2. Introduction to Physics 9th edition by: Kenneth W. Johnson
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AIG1312 Applied Physics
Grading Criteria
Assignments
Quizzes
Mid Exam
Final Exam
9/24/2024
=
=
=
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20 %
20 %
20 %
40 %
AIG1312 Applied Physics
Scalar quantity
A scalar quantity can be described by a single
number with some meaningful unit.
4 oranges
20 miles
5 miles/hour
10 Joules of energy
9 Volts
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AIG1312 Applied Physics
Vector Quantity
A vector quantity has a magnitude and a
direction in space, as well as some meaningful
unit.
5 miles/hour North
18 Newtons in the “x direction”
50 Volts/meter down
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AIG1312 Applied Physics
3-1 Vectors and Their Components


The simplest example is a displacement vector
If a particle changes position from A to B, we represent this
by a vector arrow pointing from A to B


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In (a) we see that all three arrows have the
same magnitude and direction: they are
identical displacement vectors.
In (b) we see that all three paths correspond
to the same displacement vector. The vector
tells us nothing about the actual path that
was taken between A and B.
AIG1312 Applied Physics
Vectors and Scalars
• A scalar quantity can be described by a single
number with some meaningful unit
• A vector quantity has a magnitude and a direction
in space, as well as some meaningful unit.
• To establish the direction, you MUST first have a
coordinate system!
Standard x-y Cartesian coordinates common
Compass directions (N-E-S-W)
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AIG1312 Applied Physics
Drawing vectors
• Draw a vector as a line with an arrowhead at its tip.
• The length of the line shows the vector’s magnitude.
• The direction of the line shows the vector’s direction
relative to a coordinate system (that should be indicated!)
y
x
5 m/sec at
30 degrees from
the x axis towards y
in the xy plane
z
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AIG1312 Applied Physics
Drawing vectors
Vectors can be identical in magnitude, direction, and units,
but start from different places…
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AIG1312 Applied Physics
Drawing vectors
Negative vectors refer to direction relative to some standard
coordinate already established – not to magnitude.
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AIG1312 Applied Physics
Adding two vectors graphically
Two vectors may be added graphically using the head-to-tail method.
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AIG1312 Applied Physics
Adding two vectors graphically
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AIG1312 Applied Physics
Vectors and Their Components

The vector sum, or resultant



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Is the result of performing vector addition
Represents the net displacement of two or more displacement
vectors
Can be added graphically as shown:
AIG1312 Applied Physics
Vectors and Their Components
Vector addition is commutative

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We can add vectors in any order
AIG1312 Applied Physics
Vectors and Their Components
Vector addition is associative

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We can group vector addition however we like
AIG1312 Applied Physics
3-1 Vectors and Their Components


A negative sign reverses vector
direction
We use this to define vector
subtraction
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AIG1312 Applied Physics
Components of a Vector
 Represent any vector by an x-component Ax and a y-component Ay.
 Use trigonometry to find the components of a vector: Ax = Acos θ and
Ay = Asin θ, where θ is measured from the +x-axis toward the +y-axis.
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AIG1312 Applied Physics
3-1 Vectors and Their Components



Components in two dimensions can be found by:
Where θ is the angle the vector makes with the positive x
axis, and a is the vector length
The length and angle can also be found if the components
are known
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AIG1312 Applied Physics
Calculations using Components
• We can use the components of a vector to find its magnitude
and direction:
A  Ax2  Ay2
and
tan 
Ay
Ax
• We can use the components of a
set of vectors to find the components
of their sum:
Rx  Ax  Bx Cx  , Ry  Ay  By Cy 
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AIG1312 Applied Physics