Question

As denizens of the surface of a spinning planet, we are always in uniform circular motion. Imagine you are in Nairobi (on the Earth's equator) at noon on a Monday. Answer the following questions only considering the rotation of the earth and NOT the Earth's circular motion around the sun. The radius of the earth is 6371 km. A day is 24 hours.

Assuming that you are at at theta = 0 rad at noon on Monday and moving in the positive direction, what is your position theta in rad on Tuesday at 11:00 am?

I'm assuming this has something to do with orbit and rotation, but what exactly should I be using?

Answer 1

Monday at noon to Tuesday at 11 am is 23 hours.
At Noon in Nairobi the sun is overhead on the equator (assuming on a solstice day when the sun is over the equator)
The sun stays there, but I move east with the earth rotation and 23 hours later I have gone 23/24 of the way around
(23/24)360 = 345 degrees
In another hour or 15 degrees it will be overhead again.

Answer 2

I mean an equinox, not solstice day, March or September