# Effective acceleration due to gravity in non-inertial frame

• Lost1ne
In summary, the concept of an effective acceleration in a non-inertial reference frame involves accounting for the fictitious forces present due to the acceleration of the reference frame. This allows us to accurately measure the true acceleration of a system in an inertial reference frame.
Lost1ne
Take some sort of system accelerating with respect to an inertial reference frame: let's take a spherical mass on the end of a string forming a simple pendulum with the ceiling of a car, and allow that car to accelerate uniformly.

Could someone share with me how they interpret the concept of a geffective where we take the vector sum of the fictitious force and the gravitational force acting on the mass? I don't feel as if I'm understanding it at a level that I would like to.

I'm missing something elementary here. If F_apparent = F_true - mA and A comes from F_true = mA, then we may reach the conclusion that a_apparent equals zero always. I've realized that I also used your way of thinking in the article where we add on the fictitious forces and then make the claim that our object of interest is not accelerating in our non-inertial reference frame. But, looking back at this, doesn't it not make sense for a_apparent to undisputedly equal zero? We view numerous objects accelerating through our non-inertial reference frame daily.

Lost1ne said:
...and A comes from F_true = mA,
No, F_net = ma.

A.T. said:
No, F_net = ma.
Aha. "a" is the measured acceleration of our object/system of interest from our inertial reference frame, and "A" is the acceleration of our *non-inertial reference frame with respect to our *inertial reference frame.

Lost1ne said:
Aha. "a" is the measured acceleration of our object/system of interest from our inertial reference frame, and "A" is the acceleration of our *non-inertial reference frame with respect to our *inertial reference frame.
Lets stick to lower case with subsctpt:

Fnet = Ftrue + Fapparent = mabody

Where for a linearly accelerating reference frame:

Fapparent = -maframe

Lost1ne said:
But, looking back at this, doesn't it not make sense for a_apparent to undisputedly equal zero? We view numerous objects accelerating through our non-inertial reference frame daily.
That is all correct. One is (by definition) at rest and remains at rest with respect to one's frame of reference. If you are in an elevator you will not be able to tell the difference between the following two cases: (a) The elevator is at rest near the surface of the Earth; (b) the elevator is in free space accelerating with acceleration g (relative to an inertial frame) in a direction from your feet to your head. In either case if you are standing on a bathroom scale, it will display what you know to be your true weight.

## 1. What is meant by "effective acceleration due to gravity in non-inertial frame"?

The effective acceleration due to gravity in a non-inertial frame refers to the apparent acceleration experienced by an object in a non-inertial reference frame, which is caused by the combination of the true gravitational acceleration and the acceleration of the reference frame itself. This is known as the Coriolis effect and is commonly observed in rotating or accelerating frames of reference.

## 2. How is the effective acceleration due to gravity calculated in a non-inertial frame?

The effective acceleration due to gravity in a non-inertial frame can be calculated using the formula: aeff = atrue + 2ω x v + ω x (ω x r), where aeff is the effective acceleration, atrue is the true gravitational acceleration, ω is the angular velocity of the frame, v is the velocity of the object, and r is the position vector of the object relative to the center of rotation.

## 3. How does the effective acceleration due to gravity affect objects in a non-inertial frame?

The effective acceleration due to gravity in a non-inertial frame can cause objects to appear to move in curved paths, rather than straight lines, due to the Coriolis effect. This can also result in a difference in the perceived weight of an object, as the apparent gravitational force is altered by the acceleration of the frame.

## 4. Can the effective acceleration due to gravity be eliminated in a non-inertial frame?

No, the effective acceleration due to gravity cannot be completely eliminated in a non-inertial frame. However, it can be minimized by reducing the acceleration or rotation of the frame itself, or by using a frame of reference that is as close to inertial as possible.

## 5. How does the effective acceleration due to gravity in a non-inertial frame relate to the theory of relativity?

The concept of effective acceleration due to gravity in a non-inertial frame is related to the theory of relativity, particularly the principle of equivalence which states that gravitational and inertial mass are equivalent. This means that the effects of gravity can be simulated by an equivalent acceleration, and vice versa. In a non-inertial frame, the effective acceleration due to gravity is a combination of the true gravitational acceleration and the acceleration of the frame, which is consistent with the principle of equivalence.

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