mr.p: Good morning, today we are going to review
the kinematics topics covered on the AP Physics One Exam.
Kinematics is the physics of the motion of objects
but does not include the forces causing those motions.
Bo: Hey guys.
Billy: Hey Bo. Bobby: Hi Bo.
♫ flipping physics ♫
mr.p: This being the first lecture in my review series,
I do want to make sure we cover some introductory concepts.
For example, Bo, what is the difference
between a vector and a scalar?
Bo: A vector has both magnitude and direction,
and a scalar has magnitude only.
mr.p: And Bobby, what does magnitude mean?
Bobby: Magnitude means the amount of the vector,
or the value of the vector without direction.
mr.p: Right, and this basic difference
between a vector and a scalar is one that comes up often
on AP physics tests.
For example, momentum is a vector
and I've seen many multiple choice questions
where you have a collision between two objects
and they're moving in two dimensions.
And students forget to break that momentum
into its components in the x and y directions.
And the makers of the test know this,
and they will include a multiple choice answer
that matches leaving momentum as a scalar.
So please remember the difference
between a vector and a scalar.
Speaking of vectors...
You have to remember to break or resolve vectors
into their components.
And remember that your angle theta
won't always be with the horizontal.
If theta is with respect to the vertical,
then the sin of theta which equals opposite over hypotenuse
is then equal to the vector A in the x direction
divided by vector A.
Multiplying by A we get the vector A in the x direction
equals A times the sin of theta.
Not the cosine, but the sin of theta.
So please be careful of that.
Now let's talk about kinematics.
Billy, please explain to me the difference
between distance and displacement.
Billy: Distance is just how far something moves,
and it includes the path traveled.
Displacement is the straight line distance
from where the object started to where it ended.
Bobby: Don't forget that displacement includes direction.
Bo: Displacement is also the change in position of the object.
Billy: Right, so displacement is the position final
minus the position initial, and distance is a scalar,
but displacement is a vector.
mr.p: And Bo, please give me the difference
between speed and velocity.
Bo: Isn't speed just velocity without direction?
Yeah, I'm just kidding. Billy: That's not funny.
Bo: Speed equals distance traveled over time duration,
and velocity equals displacement over change in time.
And speed is a scalar while velocity is a vector.
mr.p: And Bobby, please now tell me about acceleration.
Bobby: Acceleration equals change in velocity
over change in time, and it is a vector.
mr.p: And now let's talk about motion graphs.
Graphs of the motion of an object,
position, velocity, and acceleration
as a function of time graphs.
I haven't drawn in the lines yet, I will in a minute,
I have some questions first.
Class, what is the slope of a position versus time graph?
All: Velocity.
mr.p: What is the slope of a velocity versus time graph?
All: Acceleration.
mr.p: What is the area between the curve and the time axis
for an acceleration as a function of time graph?
All: velocity.
Bobby: No, it's change in velocity.
All: Change in velocity.
mr.p: And what is the area between the curve and the time axis
for a velocity versus time graph?
All: Change in position.
Billy: Which is displacement.
mr.p: Which is why I arranged the graphs in this order
because they are related by the slope
and the area between the curve and the time axis.
I've now drawn the blue lines
which describe the motion of this object.
Looking at the graphs, class, what can you tell me
about the motion of this object?
Bo: Because the line on the acceleration versus time graph
is horizontal, we know the acceleration
of the object is constant.
Billy: Because the velocity starts out positive
and ends negative, you can see the object
started moving upward and then fell downward.
Bobby: And as long as that is the position in the y direction,
and the acceleration is a constant
negative 9.81 meters per second squared,
then this is an object in free-fall.
It looks like the ball was thrown
vertically upward on planet Earth.
And according to the position versus time graph,
it looks like it starts and ends at the same height.
mr.p: Very nice, let's assume the acceleration
in the y direction equals negative
9.81 meters per second squared,
and we're talking about the y position.
So yes, this describes an object in free-fall.
More specifically, it has a positive initial velocity.
It is thrown upwards and it comes back down
at the very top, the slope here is zero,
therefore the velocity at the top is equal to zero.
So this is an object in free-fall with an acceleration
in the y direction equal to negative little g,
the acceleration due to gravity here on planet Earth
is positive 9.81 meters per second squared.
So the acceleration in the y direction is negative
9.81 meters per second squared, for an object in free-fall.
Which means there's nothing else touching the object,
and it's flying through the vacuum that you can breathe.
Billy: The vacuum you can breathe?
Bo: That just means no air resistance.
mr.p: Have we gone over yet any of the equations
on the equations sheet provided
for the AP Physics One Exam?
Bo: No.
mr.p: Right, so be aware there's lot to know
for the AP Physics One Exam
that is not on the equation sheet.
Now, let's go through the first three equations
on the equation sheet.
These are your uniformly accelerated motion equations.
These are the equations that describe
the motion of an object when the acceleration
of that object is uniform,
when that acceleration is constant,
when that acceleration equals a number.
I actually prefer to use the change in time,
the change in position, and specifically identify
the initial and final points, so I write them this way.
Notice on the AP equation sheet
it is assumed that time initial equals zero.
Which is how they end up using time
instead of change in time.
Also, there is one uniformly accelerated motion equation
that is not on the equation sheet.
It would probably be helpful if you learned
this uniformly accelerated motion equation,
displacement equals 1/2 times the quantity
velocity final plus velocity initial
times the change in time.
Plus when you have four UAM equations
and you remember the five UAM variables,
velocity final, velocity initial, acceleration,
change in position, and change in time,
then you can do this.
Class, there are how many UAM variables?
All: Five.
mr.p: How many UAM equations? All: Four.
mr.p: If you know how many of the UAM variables?
All: Three.
mr.p: You can figure out the other?
All: Two.
mr.p: Which leaves you with one?
All: Happy physics student! Bo: Yeah.
mr.p: I love that. Okay,
let's move on to projectile motion.
Billy, what is projectile motion
and how do we solve projectile motion problems?
Billy: Projectile motion is when an object is flying through
the vacuum you can breathe in at least two directions.
We start by splitting our known variables
into the x and y directions,
in the x direction the acceleration is zero,
so the velocity is constant.
And we can use the equation velocity equals
change in position over change in time.
In the y direction, the object is in free-fall,
so we know the acceleration equals the negative
of the acceleration due to gravity, which is then
negative 9.81 meters per second squared,
and we can use the uniformly accelerated motion
equations in the y direction.
We also know that the change in time variable
is the same in both directions because it is a scalar.
So that is what connects the x and y directions.
mr.p: Remember, if your initial velocity is neither
directly in the x direction or the y direction,
then you need to break or resolve
that initial velocity into its components.
In addition, if the initial velocity
is directly in the x direction, then the initial velocity
in the y direction is equal to zero.
Relative motion is vector addition.
Draw vector diagrams, break vectors
that are neither directly in the x or y direction
using SOH CAH TOA into their components.
Redraw the vector diagrams to make a right triangle
and then, using SOH CAH TOA and the Pythagorean theorem,
find both the magnitude and the direction
of the resultant vector.
In AP Physics One you are only responsible
for understanding center of mass
qualitatively, not quantitatively.
Bobby, what does it mean to understand
center of mass qualitatively?
Bobby: Qualitatively means we only need to understand
the concept of center of mass,
we don't have to be able to solve problems using numbers.
With numbers, that would be quantitatively.
mr.p: Correct, so you need to be able
to look at a system of objects like this one.
And know that because the object on the right
is more massive than the object on the left,
then the x center of mass of these two objects
is not located directly between the two of them,
but rather closer to the larger mass object,
and therefore approximately...
Right here. I guess you should also know,
for the purposes of translational motion,
which is a essentially non-rotational motion,
the whole object or the system of objects
can be considered to be located at its center of mass.
For example, an object or a group of objects
in projectile motion is described by analyzing
the motion of the center of mass of the object,
or the group of objects, rather than analyzing
the motion of each individual part of the object,
or each individual object in the system.
We have reached the end of my review of kinematics
for AP Physics one, my next lesson is about dynamics.
You're more than welcome to enjoy that video
and you can go to my website where you will find
all of my lectures organized with lecture notes.
Thank you very much for learning with me today,
I enjoyed learning with you.