– Good morning. Today we’re going to
review the dynamics portion of the AP Physics C Mechanics Curriculum. You know, Newtons three
laws and friction and stuff. – Don’t say, “And stuff,” just say, “Newton’s laws and friction.” ♫ Flipping Physics – Billy, what is Newton’s First Law? – When viewed from an
inertial reference frame, an object at rest will remain at rest and an object in motion will
remain at a constant velocity unless acted upon by a net external force. – An inertial reference frame is where the frame of reference
has an acceleration of zero. For example, right now,
my acceleration is zero, so this is an inertial frame of reference. A non-inertial reference frame
is where the acceleration of the frame of reference
is not equal to zero. For example, in a car, which is turning, which is a non-inertial reference frame, objects which are at rest
on the dashboard will, from the frame of
reference of the vehicle, not remain at rest. Newton’s first law is also called the Law of Inertia. And inertia is the tendency of an object to resist a change in state of motion or to resist acceleration. Bobby, what is Newton’s second law? – Newton’s second law is an equation, a net force equals mass
times acceleration, and remember force and
acceleration are both vectors. – Yes, that is the form
of Newton’s second law which I prefer, but you should be aware that has been rearranged
on the AP equation sheet to solve for acceleration. Bo, what is Newton’s third law? – Newton’s third law is also an equation. For every force object
one exerts on object two, object two exerts an equal but
opposite force on object one, and force is, of course, a vector. – Billy, what are the units for force? – Force is in newtons, and newtons are, oh, oh, net force equals
mass times acceleration. so a newton is a kilogram times
a meter per second squared. – Bobby, name and describe one of the basic forces in dynamics, please. – Okay, uh, the Force of Gravity,
the symbol is F sub g, and it equals mass times
acceleration due to gravity. It is caused by the
interaction between the object and the planet, it is always down. Here near the surface of planet earth, the acceleration due to
gravity is considered to be a constant positive 9.81
meters per second squared. It is synonymous with weight,
so sometimes you will see the symbol capital W used for
weight or Force of Gravity and it acts on the center
of mass of the object. – Actually, it acts on the
center of gravity of the object. – We live in a constant
gravitational field, so the center of gravity and
center of mass of an object are in the same place. – Sure. – Bo, another force please. – The Force Normal F sub N. It is a pushing force caused by a surface. It is normal to or
perpendicular to the surface. The Force Normal is always a push, and it acts on the contact
point between the two surfaces. – Billy, how about another force? – Another Force of Tension, capital F with a subscript of capital T, the Force of Tension is
the force caused by a rope, cable, wire, string, or the like. The Force of Tension is
always in the direction of the rope or cable, et cetera, and the Force of Tension is always a pull, and sometimes the symbol
is just capital T. There is also the Force Applied, F sub a, which is just the force of
one object pushing or pulling on another object. There is a lot we need to know
about the Force of Friction, capital F sub lower case f. It is the force caused by the interaction between two surfaces of two objects. And class, what do we
know about the direction of the Force of Friction? – The Force of Friction is
always parallel to the surfaces. – It opposes motion. – And it is independent of the direction of the Force Applied. – Yes, the Force of
Friction is always parallel to the surfaces. It always opposes motion,
and what that means is it opposes the sliding
between the two surfaces. And the Force of Friction,
the direction of it is independent of the Force Applied. Sometimes students try to tell me that the Force of Friction is opposite the direction for the Force Applied, and this is not always true. It is true that the Force Applied and the direction of the Force of Friction are independent of one another. The equation on the AP equation sheet is the absolute value
of the Force of Friction is less than or equal to mu,
the coefficient of friction, times the absolute value
of the Force Normal. There are two types of friction. Billy, please tell me about one of them. – Static Friction is when the
two surfaces are not sliding relative to one another,
and that equation works out to be the Force of Static
Friction is less than or equal to the coefficient
of Static Friction times Force Normal, and
therefore, the maximum Force of Static Friction equals the
coefficient of Static Friction times Force Normal. – Yes, the Force of Static Friction varies in an attempt to prevent the
two surfaces from sliding relative to one another. Bo, the other type of friction, please. – There is also Kinetic
Friction where the two surfaces do slide relative to one another, and then the equation is just
the Force of Kinetic Friction equals mu Kinetic times Force Normal. – Bobby, please tell me more about the Coefficient of Friction. – The symbol for the
Coefficient of Friction is mu, it is determined through experiment, it has no units. Its value depends upon the materials of the two surfaces which
are touching one another. The lowest value it could have is zero, if there is no friction. And usually the maximum is about two, however, there could be circumstances like drag racing tires where
a mu could get up to four, but really zero to two is a normal range for the Coefficient of Friction. And the Coefficient of Static Friction is greater than the
Coefficient of Kinetic Friction for any two interacting surfaces. That is why it is harder
to get something moving than it is to keep something moving. – Now let’s talk about Free
Body Diagrams or Force Diagrams. Free Body Diagrams or Force Diagrams are diagrams of all the
forces acting on objects. Again, only forces appear
in Free Body Diagrams. I have five steps to help you solve any Free Body Diagram problem. Class, step one is – [All] Draw the Free Body Diagram. – Step two. – [All] Break Forces into Components. – Step three. – [All] Re-draw the Free Body Diagram. – Step four. – [All] Sum the Forces. – And step five. – [All] Sum the Forces – Again. – One, draw the Free Body Diagram. Do not break any forces into components in your initial Free Body Diagram. These instructions come directly from the AP College
Board, so I will repeat, when you draw that
first Free Body Diagram, do not break any forces into components. Step two, break forces into components. Step three, redraw the Free Body Diagram. Now, I know many of you
are going to feel compelled to skip step number three. Please do not. I have graded copious numbers of problems from students where
they skipped step three, where they did not take
the extra 20 seconds to redraw the Free Body Diagram, and they made simple mistakes. So, please, redraw the Free Body Diagram. Steps four and five appear to be the same. But they are not. You are summing the
forces in two directions which are perpendicular to one another. Billy, what are some
things you must identify when you sum the forces? – Every time you sum the forces, you have to identify positive directions. – I thought up was positive
and down was negative. – And right was positive
and left was negative. – Yeah, that is true, I guess
if the direction is not clear, you need to identify it. Like, if there’s a pulley, for example. – Makes sense. – Okay, okay. – You also need to identify
which object or objects you are summing the forces on, and which direction you
are summing the forces in. – The only time you do
not have to identify the direction you are
summing the forces in, is when you are summing the forces in all directions simultaneously
using unit vectors. Realize the only time
you can sum the forces on multiple objects at the same time is if all those objects
have the same acceleration. For example, if they are attached, if they are connected via a string, or if one object rests
on top of another object. If an object is on an
incline, we will often, though not always, break
the force of gravity into its components in the parallel and perpendicular directions. And instead of summing the
forces in the x and y directions, we will tip the x and y directions so that we sum the forces in the parallel and
perpendicular directions. And just so you know,
theta in these equations is the incline angle. Next, let’s talk about
Translational Equilibrium. Translation Motion is
just when an object moves from one location to another. Bobby, what is the condition,
what is the equation for Translational Equilibrium? – An object is in
Translational Equilibrium if the net force acting
on the object equals zero. – That means the object is not moving. – Actually that’s not necessarily true. That means the object is not accelerating. – Right, because net force
equals mass times acceleration, so if the net force equals zero, that means the object has
an acceleration of zero. – Which means the object is either moving at a constant velocity
or is not moving at all. – But it could be not moving. – True, but it could be
moving at a constant velocity. – Another force we need to
talk about is the Drag Force or the Force of Resistance. The symbol for the resistive
force is F sub R or capital R, or F sub D. It is the force of drag
caused by the interaction between the object and the fluid through which the object is moving. The direction of the
Drag Force is opposite the direction of motion of the object, and when the object is
moving through the air, this is often called air resistance. For small objects moving at slow speeds, the force of drag is equal to the negative of the Proportionality Constant times the velocity of the object. Now, what are slow speeds
and what’s a small object? Really, the only way to know is to determine it experimentally. So for purposes of the AP test, they would either have
to tell you it’s true, or give you information and ask you to prove that it is true. Bo, please give me the
equation that we use most often for the Force of Drag. – Usually the Force of Drag
equals 1/2 times capital D, the drag coefficient of the object, which has no dimensions, is
experimentally determined, and depends on the shape and
surface texture of the object, times rho, the density of the medium through which the object is moving, times capital A, the cross
sectional area of the object, normal to the direction
the object is moving, times v, the velocity
of the object squared. – A common mistake here is to
use the density of the object. Remember, rho is the density of the medium through which the object is traveling. Our last subject is Terminal Velocity. Billy, what is Terminal Velocity? Terminal Velocity is when an
object moving through a fluid has reached translational equilibrium. May I derive the equation for the Terminal Velocity of a object which is falling downward
in the atmosphere? – Sure, Billy, go ahead. – Okay, the Free Body
Diagram of the object has the force of gravity straight down, and the resistive force straight up. Summing the forces on the
object in the y direction equals the resistive force
minus the force of gravity, and that all equals
mass times acceleration in the y direction. Substituting in the equations gives us 1/2 times the drag
coefficient of the object times the density of the air times a cross sectional area of the object times the velocity of the object squared minus the mass of the object times the acceleration due to gravity, which all equals the mass of the object times the acceleration of the
object in the y direction. We can divide by mass to solve for the acceleration of the object. And you can see that in the
absence of air resistance, the acceleration of the
object would be equal to the negative of the
acceleration due to gravity, as it should, because it
would be in free fall. Okay, but terminal velocity, the terminal velocity means
the acceleration of the object is equal to zero, so we can solve the equation
for terminal velocity, which equals the square root of two times mass times acceleration due to gravity divided by the quantity drag coefficient times density times cross sectional area. There. We derived the equation
for the terminal velocity of an object which is falling
downward through a fluid. – Yes, however, please realize
this is not the only equation for terminal velocity. This is the equation for terminal velocity in this specific case. A rocket accelerating upward, for example, would have a different
terminal velocity equation. This brings us to the end
of my review of dynamics. Next you could enjoy my review
of work, energy, and power, or you could visit my AP
Physics C Review webpage. Thank you very much for
learning with me today, I enjoyed learning with you.

## Only registered users can comment.

1. Aarti Sangwan says:

I truly enjoy learning with you!! Abbreviations for forces in AP are different sometimes T, N etc.
Everything else is perfect.

2. Senali Dias says:

thank you so very much
GOD bless

3. 廓俊傑 says:

Hello sir!
Thank you for providing these materials for us to use and study, they are very helpful!
Though I must ask if you would be willing to work on Physics C FRQs, it really helps to see someone do a video walkthough. I believe Dan Fullerton has 2016 and 2015 solutions, but I'm wondering if you could do the earlier ones like 2008 or 2007.
Thank you in advance for reading, and thank you again for these materials.

4. Du Bella says:

Great!! THANKS A LOT!!! AWESOME!!!

5. Philip Y says:

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6. Sarthak Rijal says:

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7. SunnyElsa says:

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8. Daniel Kwon says:

what does it mean by break forces into components?

9. Lightning Speed says:

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10. Kyutso Z. says:

Could you give an example of the force of friction and the force applied NOT having opposite directions?

11. SeaPeach says:

does anyone else feel satisfied every time he wrote on the board quickly?

12. Eshrit Saroop says:

Thank you so much for everything. My exam is Tomorrow. Any last minute tips? You're an amazing teacher and deserve so much more credit

13. Skylark K64 says:

14:09–

D E A D

14. Yvng Stain says:

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15. andrew oboyle says:

Thank you soooo much. You describe the material in a way thats really easy to understand