Average Angular Velocity of the Earth?

[IAmSparticus]

1. The Earth spins on its axis once a day and orbits the sun once a year (365.24 days). Take the positive direction for the angular displacement to be the direction of the Earth's motion. Express your answers in radians/second.



2. Wavg = Delta Theta / Delta Time
Delta Theta is in radians



3. Since the Earth rotates once during a day, the delta theta equals 2 Pi radians.
Time = 60 seconds (in a minute) * 60 minutes (in an hour) * 24 hours (in a day) = 84600 seconds.
2 Pi radians / 84600 seconds = 7.27 * 10^-5 rads/sec

Appartenly this is wrong accoring to the homework program WebAssign. What is wrong with my work?

Also, I got 1.99 * 10^-7 rad/sec for the angular velocity of the Earth around the sun, which is apparently also wrong.

Help?

 

[Redbelly98]

Rotation in 1 day is not exactly 2π, since in that time the Earth has moved along 1/365.24 of it's orbit.