Galilean Invariance: Determining Invariant Quantities in Newtonian Mechanics

[joriarty]

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)

Homework Equations

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?

Thank you for your help

 

[LiorE]

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.