– 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.

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

Everything else is perfect.

thank you so very much

GOD bless

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.

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

Your videos are the product of a rare talented producer with a gift for teaching!!.. thank you for all your FUN and EDUCATIONAL Videos……..

Ayyyyye. The Nice guys reference.

0:15 that sock coordination tho

what does it mean by break forces into components?

Is there any chemistry videos like this awesome videos

If yes please tell that will be helpful

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

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

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

14:09–

D E A D

Cosmo, Wanda, I wish I had some new socks

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