Okay, this is physics 1401 and i am having trouble with are coming up and my brain is malfunctioning. show me how you got the answer so i can figure it out in the future. what is the angular displacement in radians of the earth around the sun in one hour? assume the orbit is circular and takes exactly 365 days in a counterclockwise direction, as viewed from above the north pole.

The fraction of the circle that the Earth moves in that time is (1hour/1year). Massage the fraction to get the same units on top and bottom. At that point, it's just a ratio, with no units.

There are 2•π radians in a full circle, so the angle is that same fraction of 2π .

Angular displacement is measured counterclockwise anyway, so you don't have to worry about signs.

The only actual work I see here is converting 1hr to a fraction of 365da.

I'm typing on my phone right now. I'll go a little farther when I get back to my PC, if you need it.

Notice that with 365 days in a year, that means very close to 1° per day. I think it's something like 57.3 degrees in 1 radian, so the result would be something like (1/57.3) = 0.017 radian per day. Now I'll be interested to see if it's anything like this cocktail-napkin estimate, when I get back to my computer.