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PH 105 3: intro

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by

Richard Datwyler

on 26 April 2016

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Transcript of PH 105 3: intro

Kinematics in Two Dimensions:
Vectors!!!


Magnitude
Unit
Direction
Magnitude
Unit
Point to remember.

the magnitude of a vector is ALWAYS positive
the direction can be negative however.
Vectors graphically


A vector is a magnitude and direction
Are these two vectors
the same?
How about these two?
Adding Vectors graphically
A
B
Tail-to-tip method
A
B
A
B
C
C = A + B
A bit to note:
When is this true
Another special case
A
B
C
Pythagorean theorem
THIS IS KEY

This is big, the next ~7 chapters use this
We will introduce it today, and work on it
with application on Wednesday too.
Y
X
V
V
V
y
x
The idea is that every vector has
components (parts) that are in the
direction of the x and y axis.
O
Now for a bit of Trig review
O
Hypotenuse
Opposite side
Adjacent side
O
5
4
3
A. 3/4 B. 3/5 C. 4/5 D. 4/3 E.5/4
What is the cosine of theta?
What is the tangent of theta?
V
y
V
y
V
x
V
x
V
V
V
V
Sin =
Tan =
= Sin
= Cos
O
O
O
O
V
x
V
Cos =
O
y
A
B
B
A
x
x
Y
Y
B
A
x
x
A
Y
C
x
C
Y
C
B
Y
How many of these quantities do you need to define a vector?

A. 1 B. 2. C. 3 D. 4 E. depends

Vectors have:
Scalars have:
Review: Vectors and Scalars
What is this equation saying?
Another special case

A

B

C

Pythagorean theorem
Vectors: By components
Main Ideas
Vector vs. Scalar

Adding vectors as pictures, graphically, as arrows.
Math with Vectors
Adding vectors by components
Trigonometry
Projectile motion
Relative Velocity
Scalars multiply vectors
A
2A
.5A
-2A
Two big assumptions:
Ax = 0
Ay = -g = -9.8 m/s^2
Projectile motion
To describe fully this motion
they will give two terms
Launch angle
Launch speed
Relative motion
key points

Observers
measure things
can move
Constant velocity
a=0
Directions
x and y separate
Relativity is all about your point of view,
better it is about your measurement compared to someone else.
The person on the ground sees a train going 9 m/s east.

A passenger on the train is walking at 2 m/s east.

How fast does the person on the ground view the passenger?
Note the subscripts:
first letter=object
second letter = reference frame

let them form own relationship
BG ~ BT+TG ~ PG
if center two equal cut them out, and splice

The final point of relative motion is
Vab = - Vba

The magnitudes the same, direction opposite.

These two sets say the same thing.
The magnitude of a competent of a vector must be:

a) less than or equal to the magnitude of the vector
b)equal to the magnitude of the vector.
c)greater than or equal to the magnitude of the vector
d)less than, equal to, or greater than the magnitude of the vector
"I .. am,.. so lost with the adding and multiplying vectors. "
" I would like to go over resolving components of vectors a little more. "
"what is the easiest way to distinguish between scalars and vectors and know which one we are using or talking about in a problem?"
"Can you further explain relative velocity?"
"How do you find the components of a vector?"
If my velocity vector has a magnitude of 3.0 m/s
and it is at an angle of 30 degrees north of east
how much of the vector is in the 'y' direction?
a) 3.0 m/s
b) 2.6 m/s
c) 1.5 m/s
d) 0.0 m/s
e) no idea, please do this and quiz me again.
If my acceleration vector has a magnitude of 4.0 m/s^2
and it is at an angle of 30 degrees west of North
how much of the vector is in the 'x' direction?
a) 3.5 m/s^2
b) 2.0 m/s^2
c) -2.0 m/s^2
d) -3.5 m/s^2
e) 4.0 m/s^2
f)-4.0 m/s^2
"The book's definition of magnitude is a little hazy. How do you define it?"
Walk north 20 m, then walk east 10 m. Where are you?
time at 5 s, then 10 s. later, when is it?
Full transcript