For more information, please see full course syllabus of AP Physics C: Mechanics

For more information, please see full course syllabus of AP Physics C: Mechanics

### Newton's First Law & Free Body Diagrams

- Newton’s 1st Law of Motion: The velocity of an object will remain constant unless acted upon by an unbalanced force.
- Inertia is an object’s resistance to being accelerated. Mass is a measure of an object’s inertia.

### Newton's First Law & Free Body Diagrams

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- Objectives
- Newton's 1st Law of Motion
- Force
- What is a Net Force?
- What Does It Mean?
- Objects at Rest
- Objects in Motion
- Equilibrium
- Inertia
- Example I: Inertia
- Example II: Inertia
- Example III: Translational Equilibrium
- Example IV: Net Force
- Free Body Diagrams
- Falling Elephant: Free Body Diagram
- Soda on Table
- Free Body Diagram for Box on Ramp
- Example V: Translational Equilibrium

- Intro 0:00
- Objectives 0:11
- Newton's 1st Law of Motion 0:28
- Newton's 1st Law of Motion
- Force 1:16
- Definition of Force
- Units of Force
- How Much is a Newton?
- Contact Forces
- Field Forces
- What is a Net Force? 2:53
- What is a Net Force?
- What Does It Mean? 4:35
- What Does It Mean?
- Objects at Rest 4:52
- Objects at Rest
- Objects in Motion 5:12
- Objects in Motion
- Equilibrium 6:03
- Static Equilibrium
- Mechanical Equilibrium
- Translational Equilibrium
- Inertia 6:48
- Inertia
- Inertial Mass
- Gravitational Mass
- Example I: Inertia 7:40
- Example II: Inertia 8:03
- Example III: Translational Equilibrium 8:25
- Example IV: Net Force 9:19
- Free Body Diagrams 10:34
- Free Body Diagrams Overview
- Falling Elephant: Free Body Diagram 10:53
- Free Body Diagram Neglecting Air Resistance
- Free Body Diagram Including Air Resistance
- Soda on Table 11:54
- Free Body Diagram for a Glass of Soda Sitting on a Table
- Free Body Diagram for Box on Ramp 13:38
- Free Body Diagram for Box on Ramp
- Pseudo- Free Body Diagram
- Example V: Translational Equilibrium 18:35

### AP Physics C: Mechanics Online Course

I. Introduction | ||
---|---|---|

What is Physics? | 7:12 | |

Math Review | 1:00:51 | |

II. Kinematics | ||

Describing Motion I | 23:47 | |

Describing Motion II | 36:47 | |

Projectile Motion | 30:34 | |

Circular & Relative Motion | 30:24 | |

III. Dynamics | ||

Newton's First Law & Free Body Diagrams | 23:57 | |

Newton's Second & Third Laws of Motion | 23:57 | |

Friction | 20:41 | |

Retarding & Drag Forces | 32:10 | |

Ramps & Inclines | 20:31 | |

Atwood Machines | 24:58 | |

IV. Work, Energy, & Power | ||

Work | 37:34 | |

Energy & Conservative Forces | 28:04 | |

Conservation of Energy | 54:56 | |

Power | 16:44 | |

V. Momentum | ||

Momentum & Impulse | 13:09 | |

Conservation of Linear Momentum | 46:30 | |

Center of Mass | 28:26 | |

VI. Uniform Circular Motion | ||

Uniform Circular Motion | 21:36 | |

VII. Rotational Motion | ||

Rotational Kinematics | 32:52 | |

Moment of Inertia | 24:00 | |

Torque | 26:09 | |

Rotational Dynamics | 56:58 | |

Angular Momentum | 33:02 | |

VIII. Oscillations | ||

Oscillations | 1:01:12 | |

IX. Gravity & Orbits | ||

Gravity & Orbits | 34:59 | |

X. Sample AP Exam | ||

1998 AP Practice Exam: Multiple Choice | 28:11 | |

1998 AP Practice Exam: Free Response Questions (FRQ) | 28:11 |

### Transcription: Newton's First Law & Free Body Diagrams

*Hello, everyone, and welcome back to www.educator.com.*0000

*I am Dan Fullerton and today we are going to start our study of dynamics with a lesson on Newton’s first law and free body diagrams.*0003

*Our objectives are going to be to analyze situations in which a particle remains at rest*0011

*or it moves with the constant velocity under the influence of several forces.*0016

*To draw free body diagrams for objects under the influence of multiple forces.*0021

*As we talk about these let us start with Newton’s first law of motion and it is a very simple law.*0028

*Everybody thinks they know it but there as so many pieces to it and it is really tough to understand because it is tough to see here on Earth.*0034

*Let us take our time and walk through it slowly.*0039

*An object at rest will remain at rest.*0044

*An object in motion will remain in motion at a constant velocity, constant speed, and constant direction in a straight line*0048

*that is constant direction part unless acted upon by that net force or an unbalanced force.*0059

*And that is also known as the law of inertia.*0067

*What we are going to do is just dive into what that means in detail.*0069

*I suppose first we probably will talk about forces.*0074

*A force is a push or pull on an object.*0077

*The units of force are Newton's the symbol is N.*0081

*1N is 1 kg × m/s², it is a derived unit.*0085

*To give you an idea how much is in a Newton it is about the weight of a regular sized apple.*0090

*If you think of Isaac Newton sitting under a tree the apple comes down bops him on the head.*0096

*He needs all the help to remember that Newton was about the weight of 1 medium small sized apple somewhere in there.*0100

*Forces are pushes or pulls but we can divide forces into a couple different types.*0108

*We can talk about contact forces and we can talk about field forces.*0112

*Contact forces are things like that tension in a rope string pull and applied force is when you literally go push on something or pull on something.*0126

*Friction is a contact force.*0139

*All these forces that arise from the inter atomic attraction and repulsion of the electrons, the charges on atoms when we look at the very small scale.*0141

*Field forces on the other hand can act in the distance, things like gravity, the electrical force, and the magnetic force.*0154

*Electrical and magnetic are 2 different sides of the same point.*0166

*Contact forces and field forces.*0170

*What then is a net force?*0174

*Besides being a set of books by Tom Clancy and another author, a net force in physics is the vector sum of all the forces acting on an object.*0177

*Add up all the forces on an object and whenever you have left over after everything cancels out that is your net force.*0189

*It is the unbalanced force on an object.*0196

*If all the forces are balanced, if we have a 20 N force this way and 20 N force exactly opposing it our net force would be 0.*0198

*If all forces are balance there is no net force and that leads to a situation known as translational equilibrium.*0208

*Net force unbalanced force mean the same thing.*0218

*If we took an example we have some object here we have a 5 N force to the right.*0222

*We have of 5 N force to the left.*0228

*Our net force is 0.*0231

*On the other hand what happens if we have a 5 N force to the left a 3 N force to the right.*0234

*How we can find that out you can probably see just by looking at what the answer is but we can add this up in vector edition.*0246

*We would draw our 5 N force to add vectors we line them up to tail so we will move that 3 N force so it is lined up to tail there.*0253

*There is our 3 N force and our resultant goes from the starting point of the first to the ending point of the last would be 2 N to the left.*0263

*Our net force would be 2 N.*0272

*What does Newton’s first law really mean?*0276

*An object is going to continue in its current state of motion unless an unbalanced force acts on it.*0279

*Whatever it is doing it is going to keep going until there is an unbalanced force.*0285

*Objects at rest will remain at rest that is easy.*0293

*I see that all the time.*0296

*Put the cat on a couch it is going to stay there and until an unbalanced force acts upon it.*0299

*Sometimes that happens to be the dog.*0303

*Object at rest, they are still very easy to see in our world.*0307

*If we want to look at objects in motion though those will remain in motion at a constant velocity and was acted upon by a net force.*0311

*That is much harder to observe here on earth because we have so much friction.*0320

*Think about, you put a car on the highway it is going down 15 m/s and it does not just keep going 50 m/s,*0325

*unless you apply force because you have all that air resistance and the friction between the tires and the car is going to slowdown.*0333

*You just do not see this every day unless you have a very low friction apparatus you can demonstrate this with.*0339

*Instead, think of doing this in space.*0345

*Throw a baseball in space send it flying out it is going to keep going and going and going and going.*0347

*Eventually, there will be some gravitational forces on it too so we cannot get away from that unbalanced force situation but you get the idea.*0353

*Talking about equilibrium in a bit more detail.*0363

*A couple types of equilibrium.*0366

*Static equilibrium occurs when a net force on an object is 0 and the net torque on an object is 0 and it is at rest.*0368

*It is still and it does not have any net force and so it is not accelerating in any direction.*0375

*It does not have a net torque on it either.*0380

*Mechanical equilibrium occurs when a net force on an object to 0 and the net torque to 0.*0385

*That does not mean it has to be at rest that just means whatever it is doing it is going to keep doing.*0394

*Translation of equilibrium is just when a net force on an object is 0.*0399

*A couple different types of equilibrium.*0405

*Let us talk about inertia for a moment.*0409

*Inertia is the tendency of an object to resist the change in velocity.*0411

*We talked about very early mass has 2 aspects.*0416

*We have talked about inertial mass.*0420

*How hard it is to change an objects velocity?*0422

*At some measure of the objects ability to resist a change in velocity or to resist acceleration.*0426

*The other type of mass we have talked about is gravitational mass.*0433

*How strongly a gravitational field affects a mass?*0436

*We are going to get to that soon.*0438

*But every time we have measured these they have always been the same.*0440

*For the purposes of basic intro physics mass and inertia are synonymous.*0444

*Mass is a measure of an object's inertia so we can almost use those interchangeably here if you see them in a problem.*0452

*Let us take a look at an example that does just that.*0460

*Which this objects has the greatest inertia? A falling leaf, a softball in flight, a seated high school student, or a helium filled toy balloon?*0463

*And of course the object of the greatest inertia is the one that has the greatest mass.*0472

*Mass is a measure of inertia must be C our seated high school student.*0478

*Or a question like this, which of these has the greatest inertia?*0484

*A 5 kg mass moving at 10 m/s, a 10 kg mass at 1 m/s and so on and so on.*0487

*These speeds do not matter.*0495

*Inertia masses a measure of inertia.*0496

*We are just looking for the one with the greatest mass.*0500

*As we talk about translational equilibrium draw the velocity time graph for an object in translational equilibrium.*0506

*Let us start by drawing our axis.*0512

*We have a velocity on the y, time on the x, and if it is in translational equilibrium we know that the net force on the object must be 0.*0524

*Newton’s first law is going to have no acceleration, no change in velocity, no change in velocity, no acceleration means velocity must be constant.*0535

*All we have to do is draw a graph of a constant velocity, nice straight line.*0546

*Let us do a net force problem.*0559

*What is the net force of an object experiencing a pull of 5 N to the north, a push of 3 N to the south and the pull of 2 N to the east.*0561

*Let us see if we can draw that.*0573

*We got 5 N to the north, 3 N to the south, this up to the tail, 3 N to the south and 2 N to the east.*0575

*As I look at my diagram there.*0594

*If this whole thing was 5 then we came back 3 that mean this piece must be 2 N.*0596

*We got 2 N to the right and our result as we draw from the starting point of the first to the ending point of the last.*0601

*We got this 45° angle vector.*0608

*What is the magnitude of that net force?*0613

*Magnitude of our net force is just going to be if we can use the Pythagorean theorem to figure that out √ 2² + 2² is about 2.83 N.*0616

*Our angle is going to be 45° NE.*0628

*As we talk about forces of objects a very useful tool is known as the free body diagram.*0634

*It shows all the forces acting on a single object.*0641

*What we do is we draw the object itself as a dot or rectangle and then we draw all of the forces acting on that single object.*0644

*Let us take the example of the following elephant.*0653

*We have a circus elephant that falls off a tight rope, draw a free body diagram for the following elephant neglecting air resistance.*0656

*I’m going to draw an elephant as a dot quite the artist there.*0664

*Neglecting air resistance what forces act on that elephant?*0670

*The only force I can think of its following is the force of gravity which we are going to write as mg.*0675

*Draw a free body diagram for a falling elephant but this time including air resistance.*0684

*There is our elephant we still have the force of gravity on the elephant.*0690

*We also have some air resistance and air resistance is a form of friction that opposes motion.*0696

*Let us draw a force in the opposite direction.*0702

*There is our force of air resistance.*0707

*It is pretty straightforward.*0713

*Draw a free body diagram for glass of soda sitting on the table.*0716

*Let us start with a quick diagram of our situation.*0720

*We have got some table here and sitting on that we have our glass.*0725

*What are all the forces acting on our glass of soda?*0741

*Let us draw that as a dot and there is our object.*0745

*We have the force of gravity mg.*0749

*There must be another force on this.*0754

*What is that?*0757

*There is a force of table pushing back up on our glass otherwise that object will accelerate through the table and we know that does not happen.*0758

*That is what we are going to call the normal force.*0766

*The normal force is a force of perpendicular to a surface.*0771

*What is really happening is if you look very closely at the surface the atoms on that are bending down a little bit*0775

*as you have that weight on top of it and pushing back almost like a spring action.*0781

*The force when we talk about normal force, by normal we mean perpendicular.*0785

*Perpendicular force from some surface.*0795

*Those 2 we now must be exactly balance I suppose I should draw the N vector a little bit bigger because it is not accelerating at all.*0798

*It is just sitting there.*0805

*If one of those vectors were bigger than the other there would be an unbalanced force*0806

*and we would have a change in the glasses motion.*0810

*It is just sitting there it is being nice and boring and still.*0813

*How about a free body diagram for a box on a ramp?*0817

*We have a 5 kg box sitting on a ramp incline of 30° what forces act on our box?*0821

*Let us see if we can identify them first.*0828

*We can see that we are applying a force up the incline it is just sitting there it is not moving or accelerating.*0831

*We have the weight of the box, the force of gravity on it mg.*0836

*We have a normal force n and assuming it is coming up the ramp we can assume let us say*0843

*that is going up the ramp we can go in some force of friction opposing that motion right there.*0852

*Let us try out what those forces just for example problem here.*0859

*I'm going to draw my free body diagram off to the side and*0863

*the trick here when you draw your free body diagram just look at the angle of our ramp.*0867

*If it is on a ramp just use that angle of the ramp as your x axis.*0871

*Try and draw one of the axis in the direction of the object is going to move.*0874

*I could draw that is my x and my y is going to be perpendicular to my x.*0878

*Pretty close to it I suppose and you have the greatest drawing ever.*0887

*X y there is our dot for our object and that will identify the forces acting on it.*0891

*We have f up the ramp.*0898

*We have force of gravity straight down.*0901

*We got friction acting in that direction and our normal force perpendicular to the surface, perpendicular to the ramp.*0905

*There is our free body diagram but when we get into analysis of these free body diagrams forces*0916

*that do not line up with one of these axis can get a little bit troublesome mathematically.*0922

*Although this is our free body diagram what we are going to do is we are going to draw what is called a pseudo free body diagram.*0927

*Or we are going to take this vector, this force it does not line up with the axis and breaking up the components that do.*0935

*It is a little easier to deal with.*0940

*On the AP exam if you are asked for a free body diagram this is the one you have to draw.*0942

*Do not go right ahead and make a drawing that has a pseudo free body diagram even if you can do that in your head.*0948

*You will lose points.*0954

*You need to have the separate free body diagram then redraw to another pseudo free body diagram to help you with your problem solving.*0955

*Let us draw our axis again.*0964

*We will see if I can get this a little bit more perpendicular this time.*0967

*There we go we get our y and x.*0972

*We will draw our dot and we can already put the forces that lineup with the axis back on here nice and simply.*0978

*Normal force, force of friction, the only troublesome one is this force of gravity and I'm going to draw that in green*0986

*just so it stands out you make a little bigger so you can see it pretty easily.*0993

*The trick here is it does not lineup with the axis.*0999

*It would be nice if we can break it up into a component that is parallel with the x and parallel with the y.*1002

*We can do that using trigonometry.*1011

*This piece the one that is perpendicular to the ramp I will call mg perpendicular by trigonometry*1014

*we can see that that is going to be adjacent to this angle which is the same as the angle as the ramp and that is going to be mg cos θ.*1021

*This piece that is parallel with the ramp mg parallel is opposite r angle θ, the same as our angle 30° on the ramp.*1031

*That is going to be mg sin θ.*1039

*What I could do is when I redraw my pseudo free body diagram I can replace this green vector an angle*1043

*with these 2 components to make that equivalent.*1050

*I will do that here just to illustrate how we are looking were all done.*1053

*There is our y, here is our x, we will call that y x.*1058

*There is our dot.*1070

*Of course we still have f up the ramp.*1072

*We have our normal force fn or n whichever you prefer perpendicular to the ramp, the normal.*1075

*We have our force of friction.*1082

*Although we could draw it back right here from the starting point it starts to get a little tough to say.*1086

*I like to draw these n to n so I can see them a little bit better.*1090

*We have in this direction mg sin θ and over here we have mg cos θ.*1094

*That would be the useful pseudo free body diagram that I would use when I was doing a more detailed analysis of something like this.*1105

*Let us take a look at an example of how we can put all this together.*1114

*We have a 10 kg traffic light suspended from a beam as shown.*1118

*Find the tension in each of the 3 cables T1, T2, T3 supporting the traffic light.*1122

*What we will do is, let start off by looking at what we have here and I'm going to analyze our object as this one right here.*1129

*We have on that little ring, we have got T3 up as 1 force tension from the rope and we have mg down.*1139

*The net force in the y direction then let us call up the positive y is going to be all now is add up all my forces in the y.*1150

*I got T3 - mg and because it is just sitting there it is equilibrium no acceleration and net force is going to be = 0.*1159

*There is no net force, therefore, I can state that T3 = mg or T3 is going to be = m 10 kg × g round it off to 10 m/s² or 100 N.*1169

*Let us take a look at the ring itself since we have already done the right.*1187

*If we look at the ring itself, we will draw free body diagram for it and I am going to draw my axis here first.*1193

*X makes these pretty small because we have a little bit of math to do here.*1200

*Extend at the touch.*1206

*Looking here there is our object.*1210

*We have pulling on a T3 down, we have T2 to the right which we have an angle of 30° there is T2 and we have T1 up to the left then angle of 60°.*1214

*If we want to break that up for a pseudo free body diagram I am going to redraw that over here, a little bit further on the left but we do not have to do that.*1236

*Let us just keep going with our components and get through this.*1244

*The net force in the x direction if we look at this we are going to have T2 is x component which could be T2 cos 30°.*1249

*I think you can see that right from the diagram.*1257

*Going to the left we have the x component of T1 which will be - T1 cos 60° and all of that has to equal 0.*1260

*We can try the same thing for the y direction the net force in the y which just means add up all the forces in the y direction.*1271

*We are going to have T1 sin 60° + T2 sin 30° - T3 which is 100 N -100 N all has to equal 0.*1277

*Those are the equations I have to solve in order to find my tensions.*1295

*Let us take a look here and then go back to my green one my net force in x direction as it looks like that just a little bit of math I can find T1 in terms of T2.*1300

*T2 cos 30 - T1 cos 60 = 0 I could write that T2 cos 30° = T1 cos 60° or T1 is going to be equal to T2 cos 30° / cos 60° which is about 1.732 T2.*1310

*T1 is that factor × T2.*1337

*We can take that and plug that into our red equation the net force for the y direction by writing that T1 sin 60° + T2 sin 30° = 100 N,*1340

*which implies then since we know that T1 = 1.732.*1358

*T2 we can replace T1 with that so we have 1.732 T2 sin 60° + T2 sin 30° is going to be equal to r 100 N,*1364

*which implies then that when we do all that together I get 1.5 T2 + 0.5 T2 = 100 N.*1383

*Therefore, T2 must be equal to 15 N.*1395

*Once I have done that if I know T2 is 15 N I can plug that back in here for T2 to find that T1 is 1.732.*1400

*T2 which was 50 N or 86.6 N.*1410

*We found the tensions T1, T2, and T3 in our suspended traffic light.*1416

*All right hopefully that gets you a good start with Newton’s first law with free body diagram.*1427

*We are going to continue to work on these and evolve them as we go to the course.*1431

*Thank you so much for your time everyone and make it a great day.*1435

1 answer

Last reply by: Professor Dan Fullerton

Tue Jul 5, 2016 7:08 AM

Post by Hemant Srivastava on July 4, 2016

"We have a falling elephant. Oh No."

Professor Fullerton, your lessons are the first which are actually enjoyable and educational!!!

Keep being an phun physics professor!!!! :):)

1 answer

Last reply by: Professor Dan Fullerton

Mon Feb 29, 2016 6:05 AM

Post by Alexandra Baran on February 27, 2016

One medium small sized apple. ~ Professor Dan Fullerton

You are such a joker

2 answers

Last reply by: Hannah O'Neil

Thu Sep 24, 2015 9:54 AM

Post by Parth Shorey on September 22, 2015

I still didn't understand how you got T2=50N on Example V?

2 answers

Last reply by: Parth Shorey

Tue Sep 22, 2015 8:12 PM

Post by Parth Shorey on September 21, 2015

I still don't understand the difference between net force and net torque?

1 answer

Last reply by: Professor Dan Fullerton

Sun May 10, 2015 3:34 PM

Post by Aman Agrawal Aman Agrawal on May 10, 2015

in the FBD, would we write the magnitude of normal force as mg or -mg? the direction is already shown using diagram.. so we could write mg aswell?