Lecture 3: Introduction to Physics 101
Chapter 1 :
• Scalars and Vectors (1.5)
Chapter 2:
• Distance and Displacement, Speed and Velocity
(2.1,2.2)
Physics 101: Lecture 3, Pg 1
Conversion of Units – Example
A Cheetah’s acceleration when hunting
can be
a=6.1 m/s2
What is its acceleration in ft/min2 ?
Conversion factor:
1 ft = 0.3048 m
1 - 72 ft/min2
2 - 0.072 ft/min2
3 - 72 x 103 ft/min2
correct
Physics 101: Lecture 3, Pg 2
Dimensional Analysis - Example
Determine how the time t of a free fall of an object
depends on its mass m, the height h from which it
is dropped and the acceleration g due to gravity.
1 - V h/g
2 - m h/g
3 - h/g
correct
Physics 101: Lecture 3, Pg 3
Trigonometry - Example
Which one of the following expressions may be used to
correctly find the angle q ?
q
2 cm
90
5
1 - q = cos-1 (5/2)
2 - q = tan-1 (2/5)
3 - q = tan-1 (5/2)
c
m
correct
Physics 101: Lecture 3, Pg 4
Trigonometry
Right triangle:
q
adjacen
ha
t
to angle
90
hypotenuse
h
ho
opposite to angle
Definition of sine, cosine and
tangent:
Sin q = ho/h
Cos q = ha/h
Tan q = ho/ha
Pythagorean Theorem: h2 = ho2 + ha2
Any Triangle: Laws of Cosines, Sines (see E.2)
Physics 101: Lecture 3, Pg 5
Trigonometry - Example
The silhouette of a Christmas tree is an isosceles
triangle.
The angle at the top of the triangle is 30 degrees,
and the base measures 2 meters across.
How tall is the tree (in meters) ?
Physics 101: Lecture 3, Pg 6
Scalars and Vectors
Scalars are quantities which are completely
specified by their magnitude (single number+unit).
There are physical quantities which are not
completely specified by their magnitude.
Example: Displacement
Physics 101: Lecture 3, Pg 7
Scalars and Vectors
Example: Displacement
Displacement is the difference between final and initial
position of a body.
Assume a person is at an initial position A. What do you have to
specify to completely pin down the person’s final
position with respect to A ?
To be able to describe both magnitude and direction of a
physical quantity we use vectors.
Physics 101: Lecture 3, Pg 8
Vectors
Vectors are graphically represented by arrows:
The direction of the physical quantity is given by the
direction of the arrow.
 The magnitude of the quantity is given by the
length of the arrow.

Physics 101: Lecture 3, Pg 9
Addition and Subtraction of Vectors


Graphical: Tail-to-head method
Using vector components (e.g. 2 dimensional space) :
R = A+B = (Ax+Bx) x + (Ay+By) y
Physics 101: Lecture 3, Pg 10
Lecture 3:
• Scalars and Vectors
• Distance and Displacement
I strongly suggest that you try the
example problems in the textbook.
If you have trouble with any of them, please
go to office hours for help!
Physics 101: Lecture 3, Pg 11