Notes on Relativity and Cosmology - Physics Department, UCSB

38 CHAPTER 1. SPACE, TIME, AND NEWTONIAN PHYSICS
Principle of Relativity: The Laws of Physics are the same in all inertial frames.
This understanding was an important development. It ended questions like ‘why
don’t we fall off the earth as it moves around the sun at 67,000 mph?’
Since the acceleration of the earth around the sun is only .006m/s 2 , the
motion is close to inertial. This fact was realized by Galileo, quite awhile before
Newton did his work (actually, Newton consciously built on Galileo’s observations.
As a result, applications of this idea to Newtonian physics are called
‘Galilean Relativity’).
Now, the Newtonian Physics that we have briefly reviewed worked like a charm!
It lead to the industrial revolution, airplanes, cars, trains, etc. It also let to the
prediction and discovery of Uranus and Pluto, and other astronomical bodies.
This last bit is a particularly interesting story to which we will return, and I
would recommend that anyone who is interested look up a more detailed treatment.
However, the success of Newtonian physics is a story for other courses,
and we have different fish to fry.
1.8 Homework Problems
1-1. Suppose that your car is parked in front of a house. You get in, start
the engine, and drive away. You step on the gas until the speedometer
increases to 30mph, then you hold that reading constant.
Draw two spacetime diagrams, each showing both the house and the car.
Draw one in your own frame of reference, and draw the other in the house’s
frame of reference. Be sure to label both diagrams with an appropriate
scale.
1-2. Derive the Newtonian addition of velocities formula
v CA = v CB + v BA
for the case shown below where the 3 objects (A, B, and C) do not pass
through the same event. Note that, without loss of generality, we may
take the worldlines of A and B to intersect at t = 0.