# Show that Newton's 2nd Law is *Not* valid in a reference frame

• Tonia
In summary, the conversation discusses the validity of Newton's Second Law in a reference frame moving past the laboratory frame. It is shown that the law is still valid for an observer moving at a constant speed relative to the laboratory frame. The force on the object is not equal to its mass multiplied by its acceleration. The equation F=ma is used to solve the problem.
Tonia

## Homework Statement

Show that Newton's Second Law is NOT valid in a reference frame moving past the laboratory frame of problem 1 with a constant acceleration?
Problem 1: In a laboratory frame of reference, an observer notes that Newton's Second Law is valid. Show that it is also valid for an observer moving at a constant speed, small compared with the speed of light, relative to the laboratory frame.
dx^1/dt = dx/dt-v
d^2x^1/dt^2= d^2x/dt^2
force new = force old
acceleration = d^2x/dt^2 and if v is constant = dv/dt = 0

F = ma

## The Attempt at a Solution

I am not sure how to solve it

You don't have to be sure of the approach to use the approach.
Try showing that the force on the object is not equal to it's mass multiplied by it's acceleration.

## 1. What is Newton's 2nd Law and how is it related to reference frames?

Newton's 2nd Law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. This law is valid only in an inertial reference frame, where there is no acceleration or rotation. In other words, the law is valid only when the reference frame is not accelerating or rotating.

## 2. How does a reference frame affect the validity of Newton's 2nd Law?

A reference frame that is accelerating or rotating is considered non-inertial, and in this case, Newton's 2nd Law is not valid. This is because the acceleration or rotation of the reference frame affects the measurements of force and acceleration of an object within that frame.

## 3. Can you give an example of a non-inertial reference frame where Newton's 2nd Law is not valid?

An example of a non-inertial reference frame is a car making a sharp turn. The passengers in the car will feel a force pushing them towards the outside of the turn, even though there is no external force acting on them. This is due to the acceleration of the car and the reference frame being non-inertial.

## 4. Are there any other factors that can affect the validity of Newton's 2nd Law in a reference frame?

In addition to acceleration and rotation, other factors that can affect the validity of Newton's 2nd Law in a reference frame include the size and shape of the object, as well as the presence of external forces such as friction or air resistance.

## 5. How can we determine if Newton's 2nd Law is valid in a given reference frame?

To determine the validity of Newton's 2nd Law in a reference frame, we can use the concept of fictitious forces. If we observe any fictitious forces acting on an object in the frame, then we can conclude that the frame is non-inertial and Newton's 2nd Law is not valid.

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