mr.p: Good morning!
Today, we're going to go over the equations
I suggest you memorize for AP Physics I exam.
Bo: Hey guys.
Billy: Hey, Bo. Bobby: Hi, Bo.
♫ Flipping Physics ♫
mr.p: While taking the exam, you will have a copy
of the equation sheet;
however, there are plenty of equations you should memorize
that do not appear on that equation sheet.
Now, by memorize, I don't mean:
(Bobby) Sigma Li equals Sigma Lf,
but what do I do with that?
mr.p: I mean, you should have the equation memorized,
you should know what it means,
and you should know when you can use it.
For example:
(Billy) All right.
This problem is about a moon in orbit around a planet.
The net external torque acting on the moon about the planet
equals zero, which means the angular momentum is conserved,
which means the net angular momentum initial
equals the net angular momentum final,
where angular momentum is a vector.
mr.p: In my previous lessons, I went over every topic
that's in the AP Physics I curriculum.
Now, we're just going to talk about the equations
that are not on the equation sheet.
Let's begin.
Speed equals distance traveled over time duration,
velocity equals change in position over change in time,
and acceleration equals change in velocity
over change in time.
These may seem pretty basic, but they are certainly
going to come up on the exam.
If I were writing the exam, I would make sure to have
a question that tests your understanding
of the difference between speed and velocity.
Bobby: Like a problem where you determine the average speed
and average velocity for a race car
going exactly once around an oval track.
Bo: Right, the car's average velocity would be zero,
because the total displacement of the car would be zero.
Billy: But the average speed of the car would not be zero.
It would be the distance traveled
divided by how long it took.
mr.p: Displacement equals 1/2 times the quantity
velocity final plus velocity initial, times change in time,
is a uniformly accelerated motion equation
that is not on your equation sheet.
On an incline, you will often have to break
the force of gravity into its components
in the parallel and perpendicular directions.
The force of gravity perpendicular equals
the mass of the object, times the acceleration
due to gravity, times the sine of the incline angle.
And the force of gravity perpendicular equals
the mass of the object, times the acceleration
due to gravity, times the cosine of the incline angle.
Here are three useful equations having to do with energy.
Bobby, when can we use each of these equations?
Bobby: Conservation of energy can be used
when there is no work done by a force applied
or a force of friction.
Work due to friction equals the change in mechanical energy
can be used when there is no work done by a force applied,
and the net work equals the change in kinetic energy, uh...
Billy: The net work equals change in energy equation
is always valid.
Bobby: Yeah, it can always be used.
mr.p: Power equals the change in energy over change in time
is on the equation sheet;
however, it is also useful to remember
that power equals the work divided by the change in time,
which is then equal to the force doing the work,
times the displacement of the object,
times the cosine of the angle
between the force and the displacement,
all divided by change in time.
And displacement divided by change in time equals velocity.
So power also equals the force doing work on the object,
times the velocity of the object,
times the cosine of the angle
between the force and the velocity,
an equation for power in terms of velocity.
Conservation of linear momentum,
or the sum of the initial momentums
equals the sum of the final momentums,
where momentum is a vector.
Billy, when can we use conservation of linear momentum?
Billy: We can use conservation of linear momentum
when the net force acting on the system is zero,
which is during all collisions and explosions.
mr.p: Two basic circular motion equations:
angular velocity equals change in angular position
over change in time,
and angular acceleration equals change in angular velocity
over change in time.
For some reason, two uniformly angularly accelerated
motion equations did not make the equation sheet:
Angular velocity final squared equals
angular velocity initial squared,
plus two times the angular acceleration
times angular displacement,
and angular displacement equals 1/2 times the quantity
angular velocity final plus angular velocity initial,
times change in time.
When an object is moving in a circle,
it not only has an angular velocity,
but it also has a linear velocity.
That linear velocity is called a tangential velocity
because it is the velocity tangent to the circle
described by the object.
The equation is tangential velocity equals
the radius times the angular velocity.
And remember, in order to use this equation,
the angular velocity needs to be in radians.
Because these two equations are so similar,
we should talk about the velocity of the center of mass
of an object that is rolling without slipping.
It is equal to the radius of the object,
times its angular velocity.
And this is the equation for centripetal force,
or the force causing an object to move in a circle.
The net force in the in direction
equals the mass of the object,
times its centripetal acceleration,
where both force and acceleration are vectors.
And this is the equation you should use
whenever you're talking about forces on an object
moving in circular motion.
The moment of inertia, or rotational mass
of a system of particles, is equal to the sum
of the mass of each particle,
times the square of the distance from the axis of rotation.
And remember, moment of inertia is the measure
of an object or a system of particles' resistance
to an angular acceleration.
Now I guess we should talk about
conservation of angular momentum,
even though you all mentioned it earlier.
Conservation of angular momentum is valid
whenever the net external torque acting on the system
is equal to zero.
For example, when a figure skater brings in her arms,
the net external torque acting on her body
is equal to zero; therefore, angular momentum is conserved.
Therefore, because angular momentum
equals the moment of inertia times the angular velocity,
because when she brings in her arms,
that moment of inertia is decreased,
the angular velocity must increase.
The beat frequency heard when two sounds
of similar frequency occur together
is equal to the absolute value
of the frequency of one minus the other.
The net charge of an object is equal to
the excess number of charges times the elementary charge
of those charges.
In AP Physics I, you use electric potential difference
primarily in circuits; however, you do need to understand
what electric potential difference is.
Electric potential difference is the change
in electric potential energy of a charge,
divided by the charge of that charge.
The only equation for electric power on your equation sheet
is that electric power equals current,
times electric potential difference.
Remember, electric power is the rate at which
energy is being converted to heat and light
in a circuit element.
Sometimes it is also called the rate at which
energy is dissipated in a circuit element.
And using the equation, electric potential difference
equals current times resistance,
we can show that electric power also equals
the current squared times resistance,
and electric potential difference squared,
divided by resistance.
We have reached the end of my suggestions
for equations that you memorize for the AP Physics I exam.
At flippingphysics.com, you can find all of my
AP Physics I review lectures with lecture notes.
Please visit.
Thank you very much for learning with me today.
I enjoyed learning with you.
Good luck on the exam.