IB Physics Sub-topic A5 Notes

Frames of reference

In Topic A.1, you learned about the linear and circular motion of objects. Here, it was briefly mentioned that the motion of an object is relative to the observer, such that in two cars travelling at the same speed, the passengers of each do not view the other car as in motion. Thus, we say the motion of an object of often dependent on the frame of reference of the observer. A few more examples of this are:

1. A person sitting in a chair may seem motionless.
2. However, to the North pole, this person is spinning with the Earth at 460 ms^-1.
3. To the Sun, this person is orbiting around it at 29.7 kms^-1.
4. The center of the Milky Way, this person is orbiting it at 230 kms^-1.

This can keep going and going. Whilst this may just seem like an illusion of how our eyes perceive motion, it actually forms an entire branch of physics called relativistic physics. In this, you are expected to understand two types: Galilean relativity and special relativity.

Galilean relativity

Galileo developed the theory of Galilean relativity to interpret the same reference frames. The concept is to use the measurements in one frame to work out the measurements in another frame, essentially observing the comparative motion.

The standard example for this is to use two frames (F and F’), which have the directions x, y, and z and x’, y’, and z’, respectively. If a stationary observer (frame F) sees a car with a passenger (frame F’) pass by, we can determine that:

1. At any time t, frame F will be stationary and have a velocity of 0.
2. At an equal time t’, frame F’ will be moving with a velocity v’.
3. When the two graphs are overlaid to show the relative motion, it shows that F’ is moving with velocity v, which is intuitive.

This is a simple scenario because there is only movement in one plane (x-direction) and only one moving frame. However, this becomes more complicated when both observers are moving. Let’s say F is now moving towards F’.

1. At any time t, frame F have a velocity of u.
2. At an equal time t’, frame F’ will be moving with a velocity v.
3. When the two graphs are overlaid to show the relative motion, it shows that relative to one another, F and F’ are moving at a velocity of u-v. Thus: 

$u' = u-v$

To calculate their x-positions relative to one another, the formula used is:

$x' = x-vt$