Transcript Physics 101: Lecture 1 Notes

Lecture 4:
PHY101
Chapter 1 :
• Scalars and Vectors (1.5)
Chapter 2:
• Distance and Displacement, Speed and Velocity
(2.1,2.2)
Physics 101: Lecture 4, Pg 1
Vectors
Vectors are graphically represented by arrows:
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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 4, Pg 2
Addition of Vectors
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Graphical: Tail-to-head method
Resultant of Forces (Addition of Vectors)
Physics 101: Lecture 4, Pg 3
Graphical Method - Example
You are told to walk due east for 50 paces, then
30 degrees north of east for 38 paces, and then due south
for 30 paces.
What is the magnitude and direction of your total
displacement ?
Physics 101: Lecture 4, Pg 4
Addition of Vectors
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Using components (A,B lie in x,y plane):
C = A+B = Ax + Ay + Bx + By = Cx+Cy
Cx and Cy are called vector components of C.
They are two perpendicular vectors that are parallel
to the x and y axis.
Ax,Ay and Bx, By are vector components of A and B.
Physics 101: Lecture 4, Pg 5
Scalar Components of a Vector (in 2 dim.)
Vector components of vector A:
A = Ax +Ay
 Scalar components of vector A:
A = Ax x +Ay y
Ax and Ay are called scalar
components of A.
x and y are unit vectors.
Equivalently:
A=(Ax,Ay)
A is a vector pointing from the
origin to the point with
coordinates Ax,Ay.
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Physics 101: Lecture 4, Pg 6
Scalar Components of a Vector (in 2 dim.)
Scalar
components of vector A:
A = Ax x +Ay y
|A|, q known:
|Ax|= |A| Cos q
|Ay|=|A| Sin q
Ax, Ay known:
A2=(Ax )2+(AY)2
q= Tan-1 |Ay|/|Ax|
Physics 101: Lecture 4, Pg 7
Addition of Vectors
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Using scalar components (A,B lie in x,y plane):
C = A+B = Ax x + Ay y+ Bx x+ By y= Cx x+Cy y
1. Determine scalar components of A and B.
2. Calculate scalar components of C :
Cx = Ax+Bx and Cy=Ay+By
3. Calculate |C| and q :
C2=(Cx )2+(CY)2
q= Tan-1 |Cy|/|Cx|
Physics 101: Lecture 4, Pg 8
Addition of Vectors
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vector sum
Physics 101: Lecture 4, Pg 9
Displacement and Distance
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Displacement is the vector that points from a body’s
initial position to its final position. The length of is
equal to the shortest distance between the two
positions.
x = x –x0
The length of x is not the same as distance traveled !
Physics 101: Lecture 4, Pg 10
Average Speed and Velocity
Average velocity describes how the displacement of an
object changes over time:
average velocity = displacement/elapsed time
v = (x-x0) / (t-t0) = x / t
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Average velocity also takes into account the direction of
motion.
The magnitude of v is not the same as the average speed !
Physics 101: Lecture 4, Pg 11
Summary of Concepts
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kinematics: A description of motion
position: your coordinates
displacement: x = change of position
velocity: rate of change of position
• average : x/t
• instantaneous: slope of x vs. t
acceleration: rate of change of velocity
• average: v/t
• instantaneous: slope of v vs. t
Physics 101: Lecture 4, Pg 12
Lecture 3:
• Scalars and Vectors
• Distance and Displacement,
Speed and Velocity
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 4, Pg 13