AP Physics 1 & 2 Relative Motion

Hi and welcome back to Educator. com. I am Dan Fullerton.0000

This lesson is going to be about relative motion.0004

Our objectives are going to be to talk about the concept, what it means to say motion is relative and also to calculate the velocity of an object relative to various reference frames.0007

So what is a reference frame? That describes the motion of an observer.0018

The most common reference frame we are used to is the Earth.0022

The laws of physics we study in this course are going to assume we are in an inertial, non-accelerating reference frame.0026

That is not completely accurate because of the rotation of the Earth and other things having to do with the way we rotate around the sun.0035

But it is close enough for our purposes.0041

Now there is no way to distinguish between motion at rest and motion at a constant velocity in an inertia reference frame.0045

Imagine for example, you are in an airplane.0051

And once the airplane takes off, they put the windows down, the shades down on the window and it is an extremely smooth airplane. No turbulence, whatsoever.0058

As long as it is moving at a constant velocity, you cannot tell whether you are on the ground or whether you are in the air flying at a constant velocity.0070

There is no experiment you can do without having outside influences from inside the airplane that is going to tell you whether you are traveling at constant speeds or you are completely still.0078

My physics perspective, they are really the same thing.0090

Now, to talk about motion is relative, let us use an example.0096

Imagine you are sitting back in the lawn chair watching a train travel past you to the right at 50 meters per second (m/s).0099

From your reference frame, a cup of water that you would see through the trains window is moving at 50 m/s along with the train as well.0104

However, if you were sitting on that train right beside the cup of water, the cup of water would appear to be at rest.0115

Motion is relative. The velocity of that cup. The motion of that cup depends on where you are and what you are doing.0120

Now imagine, you are on the train, staring out the window, watching a student sitting in a lawn chair.0134

From your reference frame, the cup of water on the train remains still, but from your vantage point, that student sitting in the lawn chair is moving to the left at 50 m/s.0138

Again, motion is relative. So, caculating relative velocities.0148

If we consider two objects, A and B, sometimes calculating the velocity of A, with respect to reference frame B can be straightforward.0155

Such as, what is the speed of a car with respect to the ground. We are pretty good at that.0163

Or walking on a train, what is the speed of the person with respect to the train.0166

All of those are pretty straightforward.0170

But what happens if we have more objects involved?0174

Well here is a formula or a procedure that helps me understand how to do these.0176

What we are going to do, is we are going to do this in terms of an example.0182

We are going to call Object A, our cup. Object B, is a train and Object C is the ground.0185

If we want to know the velocity of Object A with respect to C, the velocity of the cup with respect to the ground, we can figure that out if we know the velocity of the cup with respect to the train plust the velocity of the train with respect to the ground.0195

So this would be the velocity of the train with respect to the ground. VAB would be the velocity of our cup with respect to the train and we're trying to find the velocity of the cup with respect to the ground.0210

A simple example, but pretty easy to do.0240

And the key here is as long as you look at the velocity of one object with respect to another, you can change any other velocities you want to as long as the middle letters keep matching.0242

A and B, B and C, what you are going to end up with is a velocity A to C.0254

So for example, if we wanted to extend this, the velocity of A with respect to E, whatever those objects are, we could find by taking the velocity of A with respect to B, plus the velocity of B with respect to C, plus the velocity of C with respect to D, plus the velocity of D with respect to E.0259

As long as these middle letters match, B to B, C to C, D to D, what you end up with is velocity of A with respect to E.0281

A little bit easier to see with some more concrete examples, so let us take a look at some of those.0294

A man travels at 60 m/s to the East with respect to the ground.0299

A business man on the train runs at 5 m/s to the West with respect to the train.0303

Let us find the velocity of the man with respect to the ground.0308

And the first thing I am going to do is I am going to identify what my different objects are.0310

I will call the train, Object A, the business man, let us call him B, and ground -- C.0316

So if we define East as positive, then the velocity, we want the velocity of the man, B, with respect to the ground.0322

Velocity of B with respect to C, must be the velocity of B with respect to A, plus the velocity of A with respect to C.0333

A is going to match up and we will get B and C.0343

So what is the velocity of B with respect to A.0346

The velocity of the business man with respect to the train is 5 m/s to the West or -5 m/s.0351

The velocity of the train with respect to the ground, well, it is 60 m/s to the East.0359

Add those vectors up, I get 55 m/s and it is positive so that must be to the East.0366

All right. Let us take another example.0376

An airplane flies at 250 m/s to the East with respect to the air.0381

The air is moving at 15 m/s to the East with respect to the ground.0386

Find the velocity of the plane with respect to the ground.0391

All right, well once again, let us identify our objects.0394

We will call the airplane, P, for plane. Let us call the air, A, and we have the ground here too, G.0396

We want the velocity of the plane, P, with respect to the ground.0405

We know the velocity of the plane with respect to the air is 250 m/s and we know the velocity of the air with respect to the ground is 15 m/s.0412

So, if we are trying to find the velocity of the plane, with respect to the ground, that is the velocity of the plane with respect to the air, plus the velocity of the air with respect to the ground.0426

Let us take a look -- our A's match up -- we will be left with BPG.0430

That is going to be 250 m/s plus 15 m/s or 265 m/s.0435

All right. Let us try one where we look at a couple of dimensions.0448

Now we have an airplane flying at 250 m/s to the East with respect to the air.0454

The air is moving at 35 m/s to the North with respect to the ground.0458

We want the velocity of the plane with respect to the ground.0464

Same thing we did before, the velocity of the plane with respect to the ground is still going to be the velocity of the plane with respect to the air, plus the velocity of the air with respect to the ground.0468

Again, those are all vectors, but what we have to remember now is they have direction.0487

So, the velocity of the plane with respect to the air, VPA, that is 250 m/s to the East.0494

The air is moving 35 m/s to the North with respect to the ground.0505

So, there is velocity, air with respect to the ground is 35 m/s.0510

We have to add these up in vector fashion in order to get the velocity of the plane with respect to the ground.0516

We have our vectors lined up tip to tail, so VPG, go to the starting point of the first, to the ending point of the last.0523

There is velocity of the plane with respect to the ground.0532

To find out what it is quantitatively -- the magnitude of the velocity of the plane with respect to the ground is going to be -- can use the Pythagorean Theorem -- the square root of 35 ² + 250 ² or about 252 m/s.0545

If we wanted to know our angle here, theta -- theta is going to be the inverse tangent of the opposite over the adjacent, 35 over 250 or about 7.97 degrees.0564

So, a two dimensional problem. Let us do one more.0575

An oil tanker, let us call it T for tanker, travels East at 3 m/s with respect to the ground, while a tugboat, B, pushes it North at 4 m/s with respect to the tanker.0581

Find the velocity of the tugboat with respect to the ground.0595

So we want velocity of the tugboat with respect to the ground -- that must be the velocity of the tugboat with respect to the tanker, plus the velocity of the tanker with respect to the ground.0600

Now what do we know? The velocity of the tugboat, VBT, with respect to the tanker is 4 m/s.0612

The velocity of the tanker with respect to the ground is 3 m/s to the East.0620

So, VBG, is going to be the vector sum, right there, just like we have done before, where that is a 3:4:5 triangle, so that is going to be 5 m/s.0629

All right a brief introduction to relative motion.0644

Hope that gets you started and on a good path.0647

Thanks for watching Educator. com. Make it a great day.0649