# Galilean Invariance: Determining Invariant Quantities in Newtonian Mechanics

• joriarty
In summary, the quantities that are invariant in Newtonian mechanics are position, distance between two points, velocity, acceleration, momentum, kinetic energy, and potential energy (assuming gravitational potential energy).

## Homework Statement

Explain which of the following quantities are invariant in Newtonian mechanics.
• Position
• Distance between two points
• Velocity
• Acceleration
• Momentum
• Kinetic Energy
• Potential Energy (I presume gravitational)

N/A

## The Attempt at a Solution

I understand that a quantity such as displacement would be invariant if a transformation is applied and that the transformed frame of reference has the same form as the original frame of reference.

However I am unsure exactly how to tackle the problem. Take for example kinetic energy, $${E}_{k}=\frac{1}{2}mv^{2}$$. How would I then determine if this was invariant or not? Can I just invent a one-dimensional transformation such as $$v'=v+a\cdot t$$ (where a is acceleration, t is time), apply this to the kinetic energy equation, and check the form of the result?

the invariant quantities in Galilean relativity are quantities that don't change when viewed from frames moving at constant velocities relative to each other, where the transformation rules are the ones given by the Galileo transformation. Try performing a general transformation on each of the quantities and see if they change or stay the same.

## 1. What is Galilean invariance in Newtonian mechanics?

Galilean invariance is the principle that the laws of motion in Newtonian mechanics are the same for all observers in uniform motion. This means that the laws of physics do not depend on the specific frame of reference of an observer.

## 2. How is Galilean invariance related to the concept of relativity?

Galilean invariance is a foundational principle of classical mechanics, which is based on the concept of relativity. This means that the laws of physics are the same for all observers, regardless of their relative motion.

## 3. What is an invariant quantity in Newtonian mechanics?

An invariant quantity in Newtonian mechanics is a physical quantity that remains the same for all observers, regardless of their frame of reference. Examples of invariant quantities include mass, energy, and momentum.

## 4. How is Galilean invariance used in practical applications?

Galilean invariance is used in various practical applications, such as in engineering and physics research. It allows us to make accurate predictions and calculations based on the laws of motion, without having to take into account the specific frame of reference of an observer.

## 5. Is Galilean invariance still applicable in modern physics?

While Galilean invariance is a fundamental principle in classical mechanics, it is not applicable in modern physics, which is described by the theory of relativity. In modern physics, the laws of motion are described by the principle of relativistic invariance, which takes into account the effects of high speeds and gravitational fields.