Frame of reference & principle of relativity

2024-10-2718:45 Status: Tags:

Moving Train, Sitting Onlookers

Imagine several people sitting in a park. They all have the same frame of reference as they are not moving relative to each other. These people may choose an origin and synchronize their clocks without issue.

Now imagine that there is a train going by at a constant velocity. The people sitting in the train are in a different frame of reference. They chose the back of the train as their origin. To the people on the train, the sitting people are moving, and to the people sitting, the people on the train are moving. Thus, people in different reference frames will generally give a different description for the same physical phenomena.

Tossing a Ball on a Train

• A frame of reference is a system of observers at rest relative to each other.
• An inertial frame is a non-accelerating frame where Newton’s 1st law holds.

The laws of mechanics are the same in any inertial referential frame

For both frames of reference, the ball obeys Newton’s laws based off of the initial conditions from and for the perspective of the observer: ${\vec{F}}_{net}=m\vec{a},p_x=cons,E_k+E_p=cons$ (ignoring air resistance, and other frictional forces). Where the path can be described by:

\\ Constant \ velocity: \ \ \ \ \ \ x(t)=(5m/s^)t \ \ \ \ \ y(t) = 3m + (0.5m/s)t + 0.5(9.81m/s^2)t^2 \end{gather}

In both cases, the object takes the same amount of time to fall for their respective frames of reference. The idea that the laws of physics are the same in two reference frames moving at a constant relative velocity is the principle of relativity. Einstein believed this to be true for electromagnetic phenomena as well.

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