Example of pendulum is inertial frame of reference or non inertial frame of reference? because if pendulum starts moving its continuously moves without changing there period of time but is changes its velocity with there motion...


closed as unclear what you're asking by Emilio Pisanty, ja72, user10851, Waffle's Crazy Peanut, Qmechanic Aug 30 '13 at 19:12

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If you search this site for "inertial frame" you'll find quite a few good questions and answers that go into exactly what an inertial frame is.

My own favourite way to find out if you are in an inertial frame is to surround yourself with a sphere of test particles. In an inertial frame, e.g. floating in space, the particles will stay as a sphere with you at the centre. In an accelerated frame, e.g. standing on Earth, the particles will move relative to you (i.e. fall to the ground), and in the presence of tidal forces the sphere will change shape.

If you surround the pendulum bob with a sphere of test particles they will all fall downwards relative to the bob, so the bob is not in an inertial frame.

Response to comment:

@mikhailcazi: if you are free falling towards the Earth then you are indeed in an inertial frame. This is one of the principles on which general relativity is built - the equivalence principle.

Actually the freely falling observer is in an only approximately inertial frame. If you watch the sphere of test particles closely you'll see it change shape due to tidal forces.

  • $\begingroup$ I don't get your methodology. If you're free-falling from a height, the test particles will still be in a sphere around you - which should mean you're an inertial frame. However, you're not, your accelerating with a magnitude of $g$! $\endgroup$ – mikhailcazi Aug 29 '13 at 10:18
  • $\begingroup$ Plus, we rarely take into account the acceleration of earth in our day to day life. If we're sitting in a stationary car, we can very well take it to be an inertial frame of reference while observing other vehicles/people/things about you. However, the test particles would say something else? :/ $\endgroup$ – mikhailcazi Aug 29 '13 at 10:21
  • $\begingroup$ @mikhailcazi: I've edited my answer to respond to your comment. $\endgroup$ – John Rennie Aug 29 '13 at 10:31
  • $\begingroup$ Wait, I worded it wrongly. Free-fall means falling when there's no force acting on a body (weight cancelled out by air-resistance). Obviously that would be an inertial frame. Suppose you were falling from a height without the effect of air-resistance. Even then wouldn't the test particles still not be moving wrt you? $\endgroup$ – mikhailcazi Aug 29 '13 at 10:56
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    $\begingroup$ @mikhailcazi: I interpreted your comment as meaning falling freely towards the Earth (without air resistance) i.e. someone standing on the Earth's surface would see you accelerating at 1g. It is the person standing on the Earth's surface who is in an accelerated frame, just as the test particles would show you. Welcome to the world of general relativity :-) $\endgroup$ – John Rennie Aug 29 '13 at 11:00

AS much i know this is

Frame of Reference

In physics, a frame of reference may refer to a coordinate system used to represent and measure properties of objects such as their position and orientation. It may also refer to a set of axes used for such representation.

Inertial Frame of Reference:-

As from the name it is the frame of reference which have some inertia or it is at rest. For example yo are standing and seeing a ball moving from left to right in a train so you see the ball from a inertial frame of reference that is you are comparing the movement of the ball from something which is stationary with respect to you.

Non-Inertial Frame of Reference:-

It the frame of reference which is not inertial or is moving. So let us say you are observing same ball in the same train but this time the train is also moving so, when you will see the ball the you will see it with the reference of the moving train that is you will not know it's actual velocity but the result of the velocities of the train and the ball velocity.

Now coming to your question:-

Now since you are are observing the pendulum so it become a object which you have to look in reference to other frame say for example the room were it is it is not a frame of reference because you are not observing anything else with respect to it. Now let us assume that the pendulum is made of glass and there is a insect inside the bob of the pendulum and now you are observing the movement of the insect. So now you are standing out and watching the pendulum moving and the insect inside it so since the pendulum is moving so you are observing the movement of the insect with respect to the moving pendulum so it is a moving frame of reference or non-inertial frame of reference. how ever if the pendulum stopped moving or you wen't inside the pendulum and then observed the insect the you are observing it's motion with respect to a inertial frame of reference or a no moving frame of reference

so weather the frame of reference is inertial or non-inertial depend's on your position to the frame of reference weather you are inside it or outside it and weather the frame of reference is moving or stationery with respect to you

Hope you got it

  • $\begingroup$ Please do not unnecessarily abuse Math Jax . I have removed the Math Jax and added 24 dollar sig6ns 4in th5e end in case you have any emotional attachment towards the dollar signs : ) . $\endgroup$ – Abhimanyu Pallavi Sudhir Aug 28 '13 at 16:36
  • $\begingroup$ haha i didn't knew that formatting so thank's and i don't have have emotional attachment with the $ haha you rock man $\endgroup$ – Dimensionless Aug 28 '13 at 16:40
  • $\begingroup$ and it didn't seem's like i abused Math Jax rather i found new way's to use it $\endgroup$ – Dimensionless Aug 28 '13 at 16:58
  • $\begingroup$ I know, but it looks ugly to have titles which stand out so much : ) . MathJax doesn't look, exactly like normal LaTeX or wiki(pedi)a LaTeX, so especially, when surrounded by a Calibri/Arial font , italicised MathJaX titles look very ugly... : ) $\endgroup$ – Abhimanyu Pallavi Sudhir Aug 28 '13 at 17:09
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    $\begingroup$ hey read the last para $\endgroup$ – Dimensionless Aug 29 '13 at 12:52

The bob of a pendulum is in a non-inertial frame as it accelerates sinusoidally. An inertial frame is precisely one that is not accelerating.


A pendulum is a non-inertial frame of reference.

What is a non-inertial frame of reference?
It is a frame of reference which has some acceleration. In these kinds of frames, Newton's laws of motion will not be applicable; hence they're called Non-inertial frames.

A pendulum is a non-inertial frame of reference because it - as you've mentioned - has different velocities at different positions, and at different periods of time. (Acceleration of a pendulum at an angle $\theta$ from the vertical is: $g\sin^2\theta$)

$P.S:$ Constant 'time period' doesn't matter. It's the value of acceleration which does.


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