Question

Describe what it means to view a moving object from a frame of reference.

Answer 1

A frame of reference is basically how everything is perceived from a certain point of view.

That is, all objects have values to describe them. They are things like velocity, position, mass, etc. In each reference frame there must be initial values, like the origin on any plot.

In most physics you've done, you usually choose the velocity and acceleration to be relative to the ground. In this inertial reference frame, the ground is at rest. And all the data falls into place.

Now, sometimes you choose to think in terms of a different reference frame. Let's look at one where we say ball 1 is at rest.

Answer 2

This switch is easy to diagram with vectors for velocity - just subtract the velocity of 1.

But it all comes from stating that our \(v_{1\text{, second frame}}\) is \(0\) and the \(v_{1\text{, first frame}}\neq0\)

If we wanted to use a coordinate system where the 1 ball is the origin, then the up/down displacement of the 2 ball is \(-3\) and of course the displacement of the 1 ball is \(\overrightarrow 0\).If we set the 2 ball to be the origin, then now its up/down displacement is \(0\) instead of \(-3\). And the up/down displacement of the 1 ball is \(3\) instead of \(0\).

All those displacement values are correct in their own reference frames! Even the the 2 ball can be viewed as 3 down, it can also be viewed as right at the origin.

You can mix things up even more. Lets say that we change what we consider to be the standard \(x\) and \(y\) directions...Now we say the 2 ball is the origin, the \(x\) and \(y\) axis are as shown, and now the \(y\) displacement of the 1 ball is 12!! But that's still acceptable, just a different frame of reference.

Now let's look at more velocities, with a popular type of example.