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 Advanced Mechanics Advanced Mechanics Physics Help Forum Nov 5th 2017, 09:24 AM #11 Senior Member   Join Date: Feb 2017 Posts: 205 Clarity on inertial reference frame. Einstein's Relativity says laws of physics are the same in all inertial reference frames. So what exactly is an inertial reference frame? We take an example. There is a person standing still on the ground and there is a truck moving with some acceleration let's say that the acceleration is a. 1. So the person standing still on the ground observes the person in the truck to be going forward with acceleration a. 2. Whereas the person in truck sees the person who is standing still going back with acceleration a. So the observation in which case is right? It's in case 1 as the truck is going forward with acceleration and the person is standing still. Whereas in case 2 the person observes the person standing still to be going back with acceleration a which is wrong! We call case 1 as inertial frame of reference and case 2 as non- inertial frame of reference. The observation in the case of non inertial frame is wrong so that's is the reason that Physics laws are not applicable to non inertial frame of reference. So if a ball is thrown horizontally by person A to Person B and Person A is stationary then the reference frame is inertial. Now what would be a non inertial frame of reference. Well that's simple, say you are commuting to somerset in a bus so you are inside the bus and the bus accelerates. This is a non-inertial reference frame. So my observation is that in order to say you are in an accelerating reference frame you should move along the moving object otherwise if you are stationary and the object is moving it is still an inertial reference frame as you are standing still. So when you throw a ball horizontally and you are still then this is an inertial reference frame. Now how does newtons first law get violated in an accelerating frame. A simple example is this: If you are in an automobile when the brakes are abruptly applied, then you will feel pushed toward the front of the car. You may actually have to extend you arms to prevent yourself from going forward toward the dashboard. However, there is really no force pushing you forward. The car, since it is slowing down, is an accelerating, or non-inertial, frame of reference, and the law of inertia no longer holds if we use this non-inertial frame to judge your motion. So you should be inside the automobile to be in an accelerating reference frame. So what Einstein means is that when you are stationary and observing the phenomenon happening, it is an inertial reference frame. This is so simple. Now I have got it.   Nov 5th 2017, 10:22 PM   #12
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 Originally Posted by avito009 Newtons all three laws are valid only in an inertial frame of reference. Here we look at newtons second law. But first, we define inertial frame of reference: An inertial reference frame is one in which a body at rest stays at rest and a body in motion continues to move at a constant velocity. So now how can F=ma be true because the formula contains acceleration and in an inertial reference frame there is no acceleration or the acceleration is zero. This is a common doubt we get. Now my explanation is this: An inertial frame of reference is one in which acceleration can be measured. So what it means is this: Lets take an example: An ball is at rest and you take the ball and throw it horizontally to another person, so initially the body is at rest so acceleration is 0. Now when the ball is thrown it accelerates 3 meters per second. So the force is equal to: say ball has a mass of a kg so F=ma= 1*3= 3 kg m/s^2. So Force is measured when there is acceleration.How? What this second law states is that initially the body is at rest but later it accelerates but after it accelerates its speed remains constant. From the above example the ball it at rest so acceleration =0. But later it accelerates 3 meters per second and stays at this speed. So this is an inertial reference frame since acceleration is measured and stays constant later. But if after the ball accelerated and later it decelerated and again it accelerated then newtons second law does not hold and force is not measurable since acceleration is not measurable. This is in laymans terms, is this correct?
Lets analyze my original post. There are two things, one is an inertial reference frame. You are the observer and you are at rest so this becomes an inertial reference frame. The second part is that in an inertial reference frame newtons first law holds. So when the ball is thrown horizontally it obeys newtons first law meaning a force is applied which makes the ball at rest move horizontally. Acceleration is 3 meters per second and mass is 1 kg so Force is 3 kg m/s^2.

Now after the ball has moves at 3 m/s its velocity is constant means the force applied is constant. So what if the force applied is not constant. This is already explained in my earlier post.

Now I get what you mean Pmb. When the force is constant, the acceleration is constant but velocity keeps changing. Aristotle thought if force is constant the velocity would be constant but this is not so. Velocity varies but acceleration is constant.

How does the ball move at constant velocity? Lets take the example of ball thrown horizontally. Here at first acceleration is required to move the body at 3 m/s but later the ball moves at constant velocity means there is no force applied, the initial force applied has gone away.

Last edited by avito009; Nov 5th 2017 at 10:34 PM.   Nov 6th 2017, 08:08 PM #13 Senior Member   Join Date: Feb 2017 Posts: 205 Constant Velocity. As mentioned by Pmb that a force is only present when acceleration is there. Take a look at the formula F= ma. We can clearly see that Force is directly proportional to the acceleration. Also when acceleration is zero Force is zero. This is how. Mass is 1 kg and initially the ball is at rest but later it is accelerated to about 3 m/s. So acceleration is 3 m/s. So force is 3 m/s. But later the velocity remains constant so acceleration is zero so plug in. F= 1*0= 0. Which proves that if acceleration is zero there is no force acting on the ball. So after the ball is thrown there is no force acting on the ball and if there was no drag which means there was no atmosphere or gravity the ball would continue to move in a straight line. As would happen in space. To move at constant velocity no force is required.   Nov 6th 2017, 09:16 PM   #14
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 Originally Posted by avito009 Now after the ball has moves at 3 m/s its velocity is constant means the force applied is constant. So what if the force applied is not constant.
Gotta poke my nose in here on two comments.
1) Newton's 2nd talks about accelerations that have an effect on motion. If an object is moving at a constant speed its acceleration is 0 m/s^2. You don't need a force to keep it moving at the same speed.

2) Check your units. I think you might be doing yourself a disservice here which may explain comment 1). Acceleration is measured in m/s^2, not m/s.

-Dan
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See the forum rules here.   Nov 7th 2017, 07:07 AM   #15
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 Originally Posted by avito009 Lets analyze my original post. There are two things, one is an inertial reference frame. You are the observer and you are at rest so this becomes an inertial reference frame.
At rest relative to what other reference frame? Any observer is "at rest" relative to himself so every observer's reference frame is "at rest". That does NOT make it an "inertial" reference frame.

 The second part is that in an inertial reference frame newtons first law holds. So when the ball is thrown horizontally it obeys newtons first law meaning a force is applied which makes the ball at rest move horizontally. Acceleration is 3 meters per second and mass is 1 kg so Force is 3 kg m/s^2.
As others have pointed put "3 meters per second" is a speed, not an acceleration. I would have thought that just a typo except for your next sentence:

 Now after the ball has moves at 3 m/s its velocity is constant means the force applied is constant.
Actually, the force applied must be 0. That is, of course, a constant but I doubt that's what you meant!

 So what if the force applied is not constant. This is already explained in my earlier post. Now I get what you mean Pmb. When the force is constant, the acceleration is constant but velocity keeps changing. Aristotle thought if force is constant the velocity would be constant but this is not so. Velocity varies but acceleration is constant. How does the ball move at constant velocity? Lets take the example of ball thrown horizontally. Here at first acceleration is required to move the body at 3 m/s but later the ball moves at constant velocity means there is no force applied, the initial force applied has gone away.   Nov 7th 2017, 10:09 PM #16 Senior Member   Join Date: Feb 2017 Posts: 205 Inertial reference frame. Lets analyze again. Inertial frames are those which are inertial relative to other inertial frames. Newton believed that a frame of reference fixed with respect to the stars is an inertial frame (Fixed stars are those that do not move relative to other fixed stars, but that does not mean they dont move, we know they move if we observe the redshift and we know universe is expanding). This was before but now for all practical purposes, any frame of reference fixed to the earth such as a railway station or a laboratory can be taken as an inertial frame. So when I say I am at rest I say this relative to the playing ground I am standing on, so relative to the playing ground my frame of reference is inertial. But when I throw the ball, this is also an inertial reference frame as compared to the inertial frame where I am at rest. A non-inertial reference frame is a frame of reference that is undergoing acceleration with respect to an inertial frame. If a bus is moving and it accelerates and you are within it. Then one reference frame is the bus station which is at rest which is an inertial reference frame and relative to this reference frame you are in a non-inertial frame of reference since you are in a bus thats accelerating. And about the acceleration part, I was refering to acceleration only it was my mistake with the units i meant m/s^2 instead of m/s. The acceleration was 3 m/s^2 since change in velocity is acceleration. Ball at rest with velocity 0 and later velocity was 3 so difference 3-0 = 3 m/s^2. Last edited by avito009; Nov 7th 2017 at 10:11 PM.   Nov 8th 2017, 02:47 AM #17 Senior Member   Join Date: Jun 2016 Location: England Posts: 841 It might seem like a circular argument but... An inertial reference frame is one in which Newtons Laws apply. Also there is no such thing as a truly inertial reference frame, just pretty close approximations. You can use Newtons laws as long as the reference frame you are using approximates an Inertial Frame closely enough that the errors are within tolerance for the problem you are working on. If your reference frame does not fit that description, then you will have to use a modified set of laws to cater for the non-inertial nature of your reference frame. __________________ ~\o/~   Nov 15th 2017, 05:21 AM   #18
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 It might seem like a circular argument but... An inertial reference frame is one in which Newtons Laws apply. Also there is no such thing as a truly inertial reference frame, just pretty close approximations. You can use Newtons laws as long as the reference frame you are using approximates an Inertial Frame closely enough that the errors are within tolerance for the problem you are working on. If your reference frame does not fit that description, then you will have to use a modified set of laws to cater for the non-inertial nature of your reference frame.
Woody! I think an inertial reference frame is one in which Newtons First Law applies. Do all newtons three laws apply in an inertial frame of reference or is it only the first law?   Nov 15th 2017, 05:43 AM #19 Senior Member   Join Date: Jun 2016 Location: England Posts: 841 The point of an inertial reference frame is that whatever test or experiment you do (where both the test and the observer remain in the same reference frame), the result will be the same regardless of any (constant) motion of the reference frame. Once you start to accelerate the reference frame, the effect of that acceleration can be detected because it will alter the results of tests (even though both the test and the observer are in the same reference frame). __________________ ~\o/~   Nov 15th 2017, 08:05 AM   #20
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There is an article on this subject in the American Journal of Physics.

On force and the inertial frame by Robert W. Brehme, Am. J. Phys., 53(10), Oct. (1985). The abstract reads as follows. From
http://aapt.scitation.org/doi/10.1119/1.14010
 Abstract The logical difficulty surrounding the definition of an inertial frame and Newtons first law of motion can be circumvented by defining the inertial frame in terms of its spatial and temporal properties, as embodied in the special theory of relativity. Whether or not these properties apply can be determined, in principle, by experiment. The mass of a body is measured through a completely inelastic collision with a body whose mass is taken as the standard. Rather than attempt to define force by a means not involving Newtons second law, we use the second law as the definition.  Tags law, layman, newtons Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post kinhew93 Kinematics and Dynamics 14 Sep 6th 2013 09:04 PM waynesplash Kinematics and Dynamics 0 Dec 16th 2011 03:12 PM FlexedCookie Kinematics and Dynamics 9 Mar 1st 2011 01:39 PM Morgan82 Kinematics and Dynamics 1 Oct 23rd 2008 09:59 AM Morgan82 Kinematics and Dynamics 1 Oct 20th 2008 05:24 PM