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