# Inertial and noninertial frame of reference examples pdf

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- Non-inertial reference frame
- Space and Time: Inertial Frames
- Non-Inertial Reference Frames
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*Reference frame , also called frame of reference , in dynamics , system of graduated lines symbolically attached to a body that serve to describe the position of points relative to the body.*

## Non-inertial reference frame

The daily rotation is quite slow: only one turn per day is 0. However, if we could observe motion over many minutes, we should notice that, for an object subject to negligible external forces, measurements made with respect to the laboratory frame show a very small acceleration. This acceleration is best considered as the acceleration of the laboratory with respect to the object: the result of the rotation of the laboratory, which turns with the Earth.

The Earth is approximately, but not quite, an inertial frame. See the Foucault pendulum and coriolis forces for a more detailed discussion of this point. Non inertial frames. In measurements made with respect to some other frames of reference, Newton's laws appear to be violated. For example, when the bus goes round a corner, a standing passenger who is not holding onto a rail seems to find himself accelerating sideways. If you try throwing and catching balls on a merry-go-round, you'll also observe some apparent violations of Newton's laws.

Try this animation: Zoe throws a ball from the centre of the a merry-go-round. To Zoe, turning clockwise with the merry-go-round picture at left , the ball seems to curve to the left - it travels anti-clockwise.

To an observer who is not rotating e. If you forget the outside world and refer everything to the frame of the merry-go-round, then you need to invent other fictitious forces which make moving objects turn. Newton's laws work in systems that are not spinning with respect to the distant galaxies. In frames of reference which spin, the 'extra forces' that have to be invoked to retain Newton's laws are fictitious forces called centrifugal forces and Coriolis forces.

For a ball thrown on the surface of the earth, the earth hardly rotates during its flight say 0. For the rather slowly swinging the Foucault pendulum , we could say that the Coriolis force makes it veer slightly to the left, and precess slowly anti-clockwise. Also in the Southern hemisphere, ocean currents and winds similarly tend to veer to the left: major circulations such as the South Pacific Current are anti-clockwise due to these Coriolis forces.

Centrifugal forces are an example of imaginary forces invented to explain motion in a non-inertial frame. Why doesn't this man fall off his bicycle? An external observer would say that he is turning and therefore accelerating to the right his left. If he could forget that he is in a non-inertial frame he might say that there is a mysterious 'centrifugal force' pushing him outwards, and he is leaning in against the force. If he sat upright on the bicycle while turning, the 'centrifugal force' would push him off the bicycle.

If he closes his eyes, can he tell whether he is upright and travelling straight, or turning and leaning inwards on the corner? A negative answer to this question is the starting point for the General Theory of Relativity, which is Einstein's theory of gravitation and accelerated motion.

But we're getting ahead of ourselves here! After one second, she is 1 metre further down the aisle. How far has she moved with respect to the platform?

This looks like a simple question, but to answer it we need to make some assumptions about time and space. Let's assume, as Galileo and Newton quite reasonably did, that time is the same for all observers, provided that they have synchronised their clocks somewhere at some time, and that rulers have the same lengths for all observers.

Okay, while I was carefully make my assumptions you beat me to it: the train has travelled 30 metres in the second, she is one metre further down the aisle, so she has travelled 31 metres with respect to the platform.

In other words In Galilean relativity, velocities add. We should point out that they add as vectors : you have to consider the angles if they are not in the same direction, but to a physicist adding vectors - things that have direction as well as magnitude - is easy enough and it's still addition. At one moment she is walking at 1 metre per second down the aisle, and a second later she is doing 3 metres per second, so her acceleration a in the train we'll assume it constant is 2 metres per second per second.

What does the man on the platform see? This is a quite important point: observers in the train and on the platform disagree about the position and velocity of our runner, but not about her acceleration. Acceleration is the same whether observed from the train or from the station. Remember that the train is travelling in a straight line at constant speed - our argument only applies to uniform relative motion.

So let's make more assumptions, no more unreasonable than those made earlier. We assume that both observers can agree on what forces magnitude F occur between her feet and the floor of the train, and that they agree on her mass m. Under Galilean relativity, if Newton's laws work on the platform, they work on the uniformly moving train.

And that is why we are confident about the animation and the experiments discussed in Galilean relativity and Newton's laws. We have more to say about inertial frames later in this presentation. For more about Newtonian and Galilean mechanics, see Physclips: Mechanics with animations and film clips. Relativity in brief Inertial frames, Newtonian mechanics and why the laws are the same in the train and on the platform Inertial frames of reference , More on Galilean relativity and Newton's laws Inertial frames Newton's laws work - sometimes.

At other times, they appear not to work. Frames of reference in which Newton's laws of motion are observed are called Inertial Frames.

## Space and Time: Inertial Frames

The daily rotation is quite slow: only one turn per day is 0. However, if we could observe motion over many minutes, we should notice that, for an object subject to negligible external forces, measurements made with respect to the laboratory frame show a very small acceleration. This acceleration is best considered as the acceleration of the laboratory with respect to the object: the result of the rotation of the laboratory, which turns with the Earth. The Earth is approximately, but not quite, an inertial frame. See the Foucault pendulum and coriolis forces for a more detailed discussion of this point. Non inertial frames.

A frame of reference is therefore a purely kinematical device, for the geometrical description of motion without regard to the masses or forces involved. For that reason an inertial frame has to be understood as a spatial reference frame together with some means of measuring time, so that uniform motions can be distinguished from accelerated motions. The laws of Newtonian dynamics provide a simple definition: an inertial frame is a reference-frame with a time-scale, relative to which the motion of a body not subject to forces is always rectilinear and uniform, accelerations are always proportional to and in the direction of applied forces, and applied forces are always met with equal and opposite reactions. It follows that, in an inertial frame, the center of mass of a closed system of interacting bodies is always at rest or in uniform motion. It also follows that any other frame of reference moving uniformly relative to an inertial frame is also an inertial frame. This appears to be a simple and straightforward concept. By inquiring more narrowly into its origins and meaning, however, we begin to understand why it has been an ongoing subject of philosophical concern.

## Non-Inertial Reference Frames

As the car maintains its acceleration, the hanging mass will not move relative to the car. We can analyze this motion from the inertial frame of reference of the ground. In this frame of reference, there are two forces exerted on the mass:.

In classical physics and special relativity , an inertial frame of reference is a frame of reference that is not undergoing acceleration. In an inertial frame of reference, a physical object with zero net force acting on it moves with a constant velocity which might be zero —or, equivalently, it is a frame of reference in which Newton's first law of motion holds. All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration. Measurements in one inertial frame can be converted to measurements in another by a simple transformation the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity. In general relativity , in any region small enough for the curvature of spacetime and tidal forces [5] to be negligible, one can find a set of inertial frames that approximately describe that region.

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Поиск занял больше времени, чем она рассчитывала. Мысли ее мешались: она тосковала по Дэвиду и страстно желала, чтобы Грег Хейл отправился домой. Но Хейл сидел на месте и помалкивал, поглощенный своим занятием.

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