Name: Graceana Kai
Physics: Inertial and Non- inertial frames of reference (rotating frames of reference) ICU PAGES 134 and 108
Date: 2013-06-15
What is relative motion? It is simply a way of saying that sometimes different people will say different things about the motion of the same object. Mind you this is not because one of these people is wrong but because these people have different frames of reference. Now this brings us to another interesting terminology, frame of reference, what is frame of reference, well, this is a coordinate system relative to which motion of an object can be observed or a coordinate system used to represent and measure properties of objects in motion, you can use frames of reference to measure velocity displacement etc.
To break it down further for those of you who find it difficult to understand this definition we can say a frame of reference can be thought of as a spot where you are doing your measurements or observation of a moving object. The best way to see how this is possible is to look at some examples.
Below is an example:
Let us say that I am standing at the back of a stationary wagon and my friend Lindsey is standing on a side walk, and I am throwing stones, each stone is thrown at 15 m/s. if you ask me at what speed I am throwing the stones at, I will say 15 m/s and if you ask Lindsey who is beside me on the side walk she will also say the stones are being thrown at 15 m/s.
Secondly, the Wagon starts to move forward at constant velocity of 20 m/s and I am still standing at the back of the wagon throwing stones, each at 15 m/s, keep in mind that everything on the wagon is travelling at 20m/s .if you ask me how fast I am throwing the stones, I will still say 15 m/s relative to me. I can only make the stones move 15 m/s away from me .But if you ask my friend on the side walk the same question, do you expect to hear the similar response? Well even before I throw a stone she will say the stones will move 20m/s which is the speed of everything on the wagon. now when I have thrown a stone forward (adding more velocity to it se will say it is going at 20m/s + 15 m/s altogether 35 m/s.
Lastly, let us say that I am still in the wagon but this time I turn around and start throwing stones from the rear backward , if you ask me again at what speed I’m throwing each stone at ,I will tell you I am throwing each stone at -15 m/s ,the reason I say negative 15m/s is because I have changed my direction .but if you ask Lindsey who is still on the side walk she will say the stones are traveling at 20m/s + (-15 m/s )=5 m/s.
What we have in this example is two different people having to different frames of reference whilst measuring the relative velocity of the same object in motion.
Furthermore, I will proceed to discuss about inertial and non-inertial frames of reference in addition rotational frames of reference. I will now discuss the two main types of inertial and non-inertial frames of reference:
What is an inertia frame of reference? An inertial frame of reference is one where the laws of physics and the laws of inertia are valid (applicable and true) .an inertial frame of reference is one which is non-acceleration (therefore it is either stationary or at constant velocity)in an inertial frame of reference the results of the measurements are always constant.

An example of an inertial frame of reference is on page 108 of the Physic 12 nelson textbook which shows an image of a bus and a ball on its floor moving at constant velocity, this example says, imagine you are sitting in a bus travelling at a constant velocity and you place a ball on the floor of the bus, notice that the ball will remain stationary and will not -move, this is a similar situation that will also occur if you were to place the ball in the classroom floor, the ball will not move because there is no external net force acting on it as you can see from this observation the laws of inertia are applicable to this situation the classroom is stationary and the bus moving at constant velocity these are good inertial frames of reference. and as for the ball, by remaining stationary it is obeying the laws of inertia (and as for you ,because you are observing this activity from inside the bus which is traveling at constant velocity, this make you an inertial observer ,also because you just witnessed the ball perform the law of inertia), now let’s say you were observing the ball from outside the bus (on the road) and the bus is still moving at constant velocity ,this still makes you an inertial observer because from outside the bus you will still be at an inertial frame of reference (on the road )the road is at stationary and therefore if you see the ball in the bus you will still be able to use the law of inertia to explain its activity. (The word inertial can be used as a hint to remind you that an inertial frame of reference is one that obeys laws of inertia).
Secondly, I will discuss non inertial frame of reference, the meaning of non-inertial frame of reference can be remembered by the hint a “no inertia”. A non-inertia frame of reference is one in which the laws of inertia and laws of physics are not applicable or not valid. I will demonstrate an example of a non-inertial frame of reference using a similar example as the one above let’s say again you are sitting in the bus that is moving at constant velocity and you place a ball on the floor of the moving bus at first the ball is still and won’t move and suddenly the driver decides to hit the brakes and the bus accelerates, the ball will move forward even though there is no net force acting on the ball this makes the bus no longer an inertial frame of reference but a non-inertial frame if reference. Non inertial frames of reference are accelerating frames of reference. Now how do you as an observer sitting inside this suddenly accelerating bus explain this movement of the ball whilst no one touched it, this is when we have to invent a pseudo force called fictitious force in order to explain this movement, and because you are in an acceleration frame of reference you the observer is known as an non inertial observer. Now imagine you were not on the bus when this entire event took place ,let’s say you were standing on the road and watching all this activity ,the activity would be easier to explain as you will now be an inertial observer ,you could say that the ball moved forward due to the fact that it was obeying the law of inertia .you can say that before acceleration the ball was moving at constant velocity with the bus then after the bus accelerates backwards, the ball moves forward trying to maintain its constant velocity just like before.
Lastly, I will discuss rotational frame of reference, what is a rotational frame of reference? Well, this is a special case of non-inertial frame of reference that is rotating relative to an inertial frame of reference. A good example of a rotating frame of reference is when you are driving in a circular path let us imagine a car traveling on a highway at first the car is travelling in a straight path, constant speed and then it decides to take a curved exit ramp leftwards, let us say you are a passenger in this vehicle, as the car takes this Curve leftwards and enters a circular path, you feel a push on your right shoulder although there is nothing physically pushing you ,this force pushes you outwards towards the car door .(once the car enters a circular path ,you become a non-inertial observer as you are now sitting in an accelerating frame of reference which is the car while trying to explain what’s happening,( remember that any object moving in a circular path is undergoing acceleration). Also you are unable to tell what is causing you to push rightwards (outwards from the circular path) and so you invent a fictitious force called centrifugal force to support your description for this movement as there is no physical origin of what you feel (using newton’s second law Fnet=Ma). on the other hand someone who can be observing the movement of the vehicle on the outside (using earth as a frame of reference would say that ,you the passenger in the car are obeying the laws of inertia as the car travels through the circular path, they would say the passengers body moves right because it wants to maintain its constant velocity ,obeying the law of inertia, this would make the outside observer in the earth reference frame an inertial observer and the Earth an inertial frame of reference, or this observer could newton’s second law (sum of all forces =Ma) to explain the situation by saying,
There is not a central force large enough to allow-the passenger to travel along a circular path. The central force would not be a made up force but a real force it could be i.e. friction, normal force and it would be known as a centripetal force.
Another type of fictitious force is called Coriolis force, it is responsible for causing the apparent deflection of moving objects when viewed in a rotating frame of reference.

Above is an image demonstrating what the direction of centrifugal force Is in a rotating frame of reference.

Above is an image demonstrating what the direction of centrifugal force is in a rotating frame of reference.

Work cited: http://cnx.org/content/m42142/1.3/ Hirsch, A. J. (2004). Nelson Physics 12: College preparation. Toronto: Thomson Nelson.