Triq radians help?

Question

Ok The earth revolves about the sun with a radius 9.3x10^7 miles....THe radius of the orbit sweeps out an angle with what exact angular velocity (in radians per hour)? How fast to the nearst hundred miles per hour is the earth traveling?

I got the answer for how fast the earht is travling by converting 1 rev of 365 days to 8760 hours then 2PI/8760 gives me pi/4380 and that is 66,705...... that rounds to 66,700 MPH the earth is travling along its orbit...

I can not get the radians per hour it is traveling am I missing something?

Answer 1

a = rx

a= arc length
r = radius
x = arc angle (has to be in radian)

so the radian per hours here is the x
a is your speed of the earth, and radius given

you should get an answer quick and simple

Answer 2

If all that you have stated is true, the earth makes a revolution in 365 days (actually this is not exact). one revolution is 2 pi radians. so you have 2 pi radians per 365 days. the rest is simple conversion
2Pi/365/24

check dimensions : radians/day/(hrs/day)=
radians/hr

Answer 3

There are 24 hours in a day and night.
There are 365¼ days in a year.

365¼ x 24hr = 8766 hr/ year.
Consider the orbit of the earth to be circular (not true but good enought for what we are doing).

Cir. of cirlce = 2π r
Cir. of cirlce = 2π(9∙3 x 10^-7)
Cir. of cirlce = 876504350∙3 miles.

Speed = Distance / time taken.
Speed = 876504350∙3 miles / 8766 hr.
Speed = 99989∙08856
Speed ≈ 100,000 miles per hour.

One orbit = 2π r
2π r = 99989∙08856 mi / hr
r = 99989∙08856/ 2π mi / hr
r = 15913∙7577 mi / hr
rad/s per hour. ≈ 15914 mi / hr