1.5 Frames of reference

Imagine…

• Your friend and yourself have set up a small experiment on your spare time, because you have nothing better to do

• Your friend stands in front of a forest – and in front of the forest is a railway track upon which is a special railcar

• This railcar contains a large window and through it you can see your friend

Imagine…

Movement

• Now, imagine that the rail car is moving at 10 km/h

• How will the scene look from your perspective (on the ground) vs. your friend’s perspective?

From the ground…

From the car…

Various views

• If you notice – depending on the viewpoint of the person involved, the velocity of the various objects in the scene will differ

• For example – take two objects in the scene – the trees, and the car itself

Are they the same?

• How would you describe the speed of the trees and the car if you were:

• Standing on the ground?• Standing in the car?

• Take the right as positive and the left as negative

What are the values?

• If you were standing on the ground:• tVg = 0 km/h• cVg = 10 km/h

• If you were standing on the railway car:• tVg = -10 km/h• cVg = 0 km/h

Frame of reference(FOR)

• Notice that the velocity of the objects were different depending on where you are observing the event

• A frame of reference refers to the point of view that you are choosing to analyze an event

Important things to consider regarding a frame of reference

• In a given FOR, the type that we will be focusing on are ones in which no acceleration takes place

• This is known as an INERTIAL FOR• In an inertial FOR, all the laws of

physics will apply

For example…

• Imagine you find yourself in a room – you are sitting in apparatus that cushions you from all movement

• There is a ball sitting still on a table• The ball doesn’t move• And you notice that when you drop a

ball from where you sit, it falls to the ground

But what if…

• In the same room, the ball on the table suddenly flies forwards?

• Or if when you try to drop a ball on the ground, it doesn’t take a straight path to the floor?

• HOW WOULD YOU EXPLAIN THIS?

What if the car was moving?

• In the first situation, the room that you were sitting in could be either completely still or moving at a constant speed – both would produce those results

• Think about sitting in a car that is moving smoothly at a constant speed – and throwing a ball up and down or placing it on the seat

What if the car were to stop?

• Now imagine sitting in that same car, and suddenly, the driver slams on the brakes

• What would happen if you were trying to catch a ball that you just threw upwards, or a ball that was placed on the edge of the seat?

Non-inertial FOR

• In non-inertial FOR, the FOR experiences a change in motion

• Since the laws of physics don’t apply in non-inertial FOR (think – objects don’t suddenly slide off tables without a visible force applied) it becomes hard to compare it with an inertial FOR

• For many of the relative velocity questions we deal with, we assume that all FOR’s are inertial

Relative velocity

• Therefore, velocity of an object can change depending on the FOR that you choose to analyze it from

Moving within a FOR

• There are 2 basic types of relative velocity that we are going to look at – and therefore, 3 basic types of relative velocity questions that you are going to come across

• One type is relative velocity in ONE DIMENSION – that can be thought about by looking at the railway track example again

Imagine…

• What would happen if your friend began walking towards the back of the railway car at 6 km/h as it passed you at 10 km/h?

• Would your friend’s speed look the same as from your point of view as it did before?

One dimensional FOR

Notice…

• That your friend’s velocity relative to the ground DECREASED

• Because they were moving towards the back of the car, their backwards velocity is subtracted from the forward velocity of the car

• How would your friend’s velocity appear to you if your friend was moving towards the front of the car?

One dimensional FOR

Two-dimensional FOR

• In a 2D FOR, motion can occur on a plane

• An outside “force” pushes the object, and contributes a velocity vector that provides a perpindicular direction to the object’s motion

If you are standing on the shore and watching, what will happen to a swimmer that tries to travel across the water?

If you are the swimmer – what is your direction relative to the water?What is the water’s direction relative to the ground?

sVw

wVg

sVg

Notice…

• In 2D vector questions, there are 3 vectors that are described•fVg: The force’s (water, wind, another

moving FOR, etc.) velocity relative to the ground

•oVf: The object’s (ship, boat, swimmer, etc.) velocity relative to the force

•oVg: The object’s velocity relative to the ground

Limited situations…

• In general, most of the questions you will encounter are limited in how these vectors can be oriented relative to each other

• Ofcourse, like all basic vector questions, 3 vectors means that you can create either a right angled or non-right angled triangle

And in real life…

• There is only a few ways that a force and an object can interact to create the various types of vector questions that you’re going to see

• Therefore, there are 2 basic situations that you will come across when solving relative velocity questions

“Push”

• In these types of questions, the force pushes the object away from the original path that the object wanted to take

• This is the example that we have seen earlier

Notice how the swimmer’s body is oriented – they face the shore and swim – so although the body faces towards the shore, the body takes a diagonal path across the water

oVf

fVg

oVg

“Fight”

• In these types of questions, the object is trying to oppose the force to follow a particular path

oVf

fVg

oVg

Notice how the swimmer’s body is oriented – they turn their body so that they swim diagonally relative to the water – but the water pushes the swimmer back so that their velocity relative to the ground is directly across the river