Physics 20: 2.1 Vector Directions
Summary
TLDRThis educational video script introduces the concept of vectors in physics, focusing on understanding direction systems. It explains the Cartesian coordinate system's directional approach starting from zero degrees and the navigation system using north, east, south, and west. The script emphasizes the importance of identifying vector directions from verbal descriptions to solve problems involving trigonometry and angle calculations. It also clarifies the difference between 'north 30 degrees east' and 'east 30 degrees north,' illustrating how to convert between various directional notations for consistency in problem-solving.
Takeaways
- 📚 The lecture begins with an introduction to vectors and the importance of understanding direction in physics.
- 🧭 The main strategy for dealing with vector questions involves breaking vectors into their horizontal and vertical components using trigonometry.
- 📐 Trigonometry will be used to solve for angles and missing sides, with sine and cosine being fundamental to finding the components of a vector.
- 📏 The Cartesian coordinate system is used for direction in physics, with angles measured from the positive x-axis (0 degrees).
- 🌐 The navigation system uses cardinal directions (north, east, south, west) to specify vector directions, such as 'North 30 degrees east'.
- 🔍 Locating the direction of a vector is crucial, as questions often describe directions in words rather than providing triangles.
- 📊 When a vector is given in terms of degrees, the reference angle is used to simplify the trigonometric calculations.
- 🔄 Understanding the complementary angles is important, as they can be used to convert between different directional descriptions.
- 🌡 The navigation system can describe directions in a variety of ways, such as 'North 45 East' or 'East 45 North', which are equivalent.
- 📍 The script emphasizes the need to be able to interpret and draw vector directions from verbal descriptions to solve physics problems.
- 📘 The lecture also mentions that different materials might use different conventions for writing angles, such as '40 degrees north of West'.
Q & A
What is the main strategy for solving vector problems in physics as described in the transcript?
-The main strategy for solving vector problems in physics, as described in the transcript, is to break the vector into its horizontal and vertical components. This simplifies the process of solving for angles and missing sides using trigonometry.
How does the transcript suggest breaking down a vector like a speed of 10 meters per second at 30 degrees?
-The transcript suggests using trigonometry to break down the vector. For a speed of 10 meters per second at 30 degrees, you would use sine and cosine functions to find the vertical (y) and horizontal (x) components, respectively. Specifically, y = 10 * sin(30) and x = 10 * cos(30).
What is the Cartesian coordinate system used for in the context of the transcript?
-In the context of the transcript, the Cartesian coordinate system is used to determine the direction of a vector. It starts with 0 degrees on the right side, then goes up to 90 degrees at the top, 180 degrees on the left, and 270 degrees at the bottom.
How does the transcript describe the process of locating a vector direction in physics?
-The transcript describes the process of locating a vector direction by starting from the zero degree mark and measuring the angle from there. For example, a vector going 10 meters at 70 degrees would be drawn starting from the origin and measuring 70 degrees upwards.
What is the reference angle mentioned in the transcript, and how is it used?
-The reference angle mentioned in the transcript is the smallest angle between the terminal side of an angle and the x-axis. It is used to determine the direction of a vector when the angle is greater than 90 degrees or less than 270 degrees. For example, a 350-degree angle has a reference angle of 10 degrees.
How does the navigation system for directions differ from the Cartesian system discussed in the transcript?
-The navigation system for directions, as discussed in the transcript, uses cardinal directions like north, east, south, and west instead of the mathematical degrees used in the Cartesian system. It involves determining the direction of a vector based on angles from these cardinal points.
What does the transcript mean by 'North 30 degrees east' in the context of the navigation system?
-In the context of the navigation system, 'North 30 degrees east' means that the vector is directed towards the north first and then moves 30 degrees from the north towards the east to determine its exact location.
How can you convert a direction like 'South 65 degrees west' into its corresponding angle in the Cartesian system?
-To convert 'South 65 degrees west' into its corresponding angle in the Cartesian system, you would draw the vector starting from the south and then measure 65 degrees towards the west from that starting point.
What is the significance of the complementary angle in the context of the transcript?
-The significance of the complementary angle in the context of the transcript is to help convert between different directional systems. For example, if you have 'North 30 degrees west' and you need 'West 30 degrees north', you can use the complementary angle (60 degrees) to find the equivalent direction.
How does the transcript explain the difference between 'North 30 degrees west' and 'West 30 degrees north'?
-The transcript explains that 'North 30 degrees west' means moving from the north towards the west by 30 degrees, while 'West 30 degrees north' means moving from the west towards the north by 30 degrees. These are not the same direction, and the difference lies in the starting point and the direction of the angle.
What is the reference to '40 degrees north of West' in the transcript, and how does it relate to the navigation system?
-The reference to '40 degrees north of West' in the transcript is an alternative way of expressing directions, where you start from the west and then move 40 degrees towards the north. It is related to the navigation system and is equivalent to 'West 40 degrees north'.
Outlines
📚 Introduction to Vectors and Direction Systems
This paragraph introduces the concept of vectors in physics, emphasizing the importance of understanding direction systems before delving into vector calculations. The speaker explains that vectors can represent various physical quantities like displacement or speed, and gives an example of a vector with a magnitude of 10 meters per second at an angle of 30 degrees. The main strategy discussed is breaking down vectors into their horizontal and vertical components to simplify problem-solving. The paragraph also touches on the basics of trigonometry that will be used, such as sine and cosine, and the challenge of visualizing and drawing triangles based on word descriptions rather than given geometric figures. The Cartesian coordinate system is introduced as the first method for direction, starting with zero degrees on the right and moving counterclockwise to 90, 180, and 270 degrees.
🧭 Understanding Cartesian and Navigation Direction Systems
The second paragraph delves deeper into the two primary direction systems used in physics: the Cartesian system and the navigation system. The Cartesian system is familiar to those who have studied trigonometry, where directions start from the zero degree mark on the right and move counterclockwise. The navigation system, akin to GPS, uses cardinal directions (north, east, south, west) to specify the direction of a vector. The paragraph provides examples of how to interpret and draw vectors described in these systems, such as 'North 30 degrees east' or 'South 65 degrees west'. It also explains how to convert between different directional descriptions, like 'North 30 degrees west' and 'West 30 degrees north', by using complementary angles. The speaker clarifies that certain directional descriptions can be interchangeable, such as 'north 45 East' or 'east 45 North', but others are distinct and require careful interpretation. The paragraph concludes by noting that different materials may present angles in various ways, such as '40 degrees north of West', which should be understood as equivalent to the navigation system's description.
🔍 Comparing and Equating Directional Descriptions
This paragraph continues the discussion on direction systems, focusing on equating different ways of describing the same direction. The speaker illustrates how various directional phrases can point to the same location, such as '60 degrees west of North', 'West 30 degrees north', and '150 degrees in the math Cartesian system', emphasizing that they all represent the same vector direction. The paragraph also addresses potential confusion with terms like 'north of West' and 'south of East', explaining that these can be rearranged or converted to understand the direction better. For instance, '35 degrees south of East' can be understood as 'East 35 South'. The speaker encourages students to be adept at visualizing and drawing any directional scenario, regardless of how it is described, to ensure they can accurately determine the vector's direction.
Mindmap
Keywords
💡Vectors
💡Direction System
💡Trigonometry
💡Displacement
💡Speed
💡Horizontal and Vertical Components
💡Cartesian System
💡Navigation System
💡Reference Angle
💡Complementary Angle
Highlights
Introduction to vectors in physics and the importance of understanding direction systems.
The necessity of locating a vector's direction accurately in physics problems.
Breaking down vectors into horizontal and vertical components for easier problem-solving.
Incorporation of trigonometry in vector analysis with simple sine and cosine applications.
Understanding the Cartesian coordinate system as it applies to physics.
The concept of zero degrees starting on the right side in the Cartesian system.
Locating vectors based on angles in the Cartesian system, such as 70 degrees.
The process of determining vector locations in terms of degrees, like 220 degrees.
Using reference angles in the Cartesian system, such as 350 degrees equating to 10 degrees.
The navigation system in physics, which uses north, east, south, and west for direction.
Interpreting navigational vectors, such as 'North 30 degrees east'.
Understanding the difference between 'South 65 degrees west' and other directional vectors.
The concept of complementary angles in navigational directions, like 'North 30 degrees west'.
Identifying equivalent directional vectors, such as 'North 45 East' and 'East 45 North'.
The distinction between 'North 30 degrees West' and 'West 30 degrees North'.
Dealing with different directional notations like '40 degrees north of West'.
Recognizing equivalent directional scenarios in various systems, such as '60 degrees west of North'.
Transcripts
okay so we're our next units on vectors
we're going to start with vectors but
before we get to looking at Vector
questions and doing some trigonometry
and solving for angles and missing sides
and stuff like that we have to be clear
on how our Direction system works for
physics so the first thing that you got
to be careful of is when you see
something with a direction you have to
be able to locate where that exactly
would be so most of the questions we're
going to get this for this unit is
you're going to get a some sort of
vector so it could be a displacement or
a speed or whatever so let's just
suppose it was 10 meters per second
and then they're going to tell you
that's going to go at some sort of angle
so let's suppose
it was at 30 degrees
what we're going to want to do is be
able to
break that Vector into horizontal and
vertical components then we could
basically solve the questions a lot
easier so that's going to be our main
strategy so we're going to be getting
into the trigonometry and stuff later on
so basically the as hard as the Trig's
ever going to get is
you would get sine 30
would equal in this case the red let's
call it X we'd have or let's call it y
it doesn't matter which one's which
so let's for now just keep it sort of
simple let's call that our y direction
so we'd have y divided by 10 and then on
the bottom we'd have cosine of 30.
equals adjacent over hypotenuse so X
over 10. so that's what is complicated
as the trigonometry is going to get for
this stuff which is good everybody's
done this before the hard part is
locating that direction they're not
going to give you the triangles usually
it's going to be in words so you have to
be able to draw the triangles and figure
out the directions on your own
so the first
first topic that we're going to look at
are the first way of doing directions is
based on the Cartesian system which is
what we use in math so those of you
doing math 20-1 you would have done this
already in the trigonometry unit
so what we do with the math directions
is we always start at the zero degrees
over on the right side then we go up to
90 degrees on the top 180
and 270.
so in physics if the question was you're
going to go 10 meters
at 70 degrees
then what we would do is that means
we're going to be drawing this thing
from the zero we measure 70 degrees
upwards
so that would be where our Vector would
be and then from there we could figure
out our
vertical and horizontal components if we
need to so that's the first one 10
meters at 70 degrees and for today we're
not going to worry about the 10 meters I
just want to worry about the
the where the location would be so the
next one is let's suppose I told you we
have something located at 220 degrees
so the 220
would be we'd go around to the 180 and
then we'd add on a little bit more and
that would get us
to 220. so the 220 degrees would look
something like that and then later on
when we do the trig calculations we're
not going to worry about the 220 we're
going to basically make our triangle
out of that and then we'd use 220 minus
80 we'd use 40 degrees
inside our triangle
okay so let's do a couple more so
wirewood
350 degrees be located well that's going
to be all the way around
just not quite to the 360 which would be
the zero location so that would be about
10 degrees like that or
350 all the way around okay so math
terms we call those the reference angle
so we're 350 degrees goes all the way
around our reference angle would be the
10 degrees that we're going to work with
and let's do one more let's suppose we
had an angle of
140 that's going to be
something like that
so our reference angle in this case
would be 40 degrees down there
okay so those of you that are doing this
in math this will seem familiar okay so
you'll find this this system pretty
basic and pretty easy you just have to
make sure you always go from the zero
and measure your way around
the next system we're going to look at
is probably I don't know if it's used
more than the other one but it's used
quite a bit in physics and this is the
navigation one and in this case this is
like a GPS system where we use
north east south and west instead of
the math system so in this case you're
going to get questions where they'll say
things like we have a vector going at
North
30 degrees east
okay so what you have to do is you have
to be able to figure okay what is that
where's that location so in this sense
the first letter is telling you we're
going towards the North First
and then we're going to be moving 30
degrees from there towards the east
so in terms of drawing our triangle it
would look something like that where 30
degrees would be down there so from the
north towards the east that would be
where our angle would be okay so let's
do a couple more of those so if I gave
you
South
65 degrees west
that means we're going to be moving from
the south towards the west and we're
going to go
65 degrees so it would look something
like that
all right if I gave you let's do one
more let's do
East
20 degrees south
so just similarly we'll be heading
towards the east first so from the East
towards the South we're gonna go
20 degrees
okay so that's sort of the navigation
system and they work pretty good if you
get a question that just says
um
Northeast only
then that means it's perfectly right
down the middle so that would be 45
degrees Northeast or 45 degrees east of
North so if you get two angles so let me
just write that one so if I go north 45
East
or east 45 North because they're both 45
degrees those are exactly the same thing
so there's no difference in either way
that's why we can just write it as
Northeast and it doesn't make any
difference
but if I gave you
let's do a different one if I gave you
North
30 degrees west
and I give you West 30 degrees north
those are not the same
okay those aren't the same because North
40 30 degrees west would be
from the north towards the west 30
degrees and west 30 degrees north would
be down here it would be 30 degrees
upwards from the West so those aren't
the same but what you could do if you
get one and you need to figure out the
other is instead of being North 30
degrees West and West 30 degrees north
all you'd have to do is change the other
one to the complementary angle so if
this angle up here is 30 that means the
one below it would be 60. so North 630
degrees West and West 60 degrees north
those are the same okay and it wouldn't
matter on a test if you're writing them
either one would be acceptable
there's one other thing we got to look
at when we're dealing with these I'll
just start a new page
so if we get a
Direction system like that in the
textbook and in other older materials
quite often they'll write the angles
instead of the way we just wrote them
they'll write them as 40 degrees
north of West
so in this case it says 40 degrees north
of West we're going from the West
towards the north north of West so in
this case that 40 degrees north and west
would be like that
and if you use the one that we just
looked at we said we're heading west
then going 40 degrees north so that
would be those two things are the same
so some people get mixed up with this
north of West South of East so if you
ever do that if I gave you a question
that was 35 degrees
south of East
if you want you can switch it to the
other around move the East to the front
see that East 35 South
and those two things would be the same
so East 35 South would be from the East
towards the South 35 degrees
or if you can understand 35 degrees
south of East
that's the same so either one both of
those systems are good you're going to
see questions where they're all mixed up
so you just have to be able to sort of
draw any kind of scenario
so if I gave you a different one that I
said
[Music]
60 degrees west
of North
or I told you to draw West 30 degrees
north or I try to tell you to draw 120
in the math Cartesian system you should
see that these are all the same thing so
60 degrees west of North
would be
60 degrees west of North would be like
that right from the north we're going 60
degrees towards the west or the other
one West 30 degrees north so from the
West we're going to head 30 degrees to
the north would be there and I messed up
on the last one it shouldn't be 120 it
should have been
150. so if we measure in the math system
150 degrees
would go all the way around and we'd get
to there so all three of those are the
same it doesn't matter which one you'd
be given you're going to see that
they're all exactly the same location so
any particular question could use any of
the three
locations
تصفح المزيد من مقاطع الفيديو ذات الصلة
5.0 / 5 (0 votes)