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.

 

[kerimek]

There are a few errors in your calculations that may be causing the discrepancies in your answers. First, the time for a day should be 24 hours, not 84600 seconds. This would result in an average angular velocity of 7.27 * 10^-5 rads/sec for the Earth's rotation on its axis.

Secondly, for the Earth's orbit around the sun, the time should be 365.24 days, not 365.24 seconds. This would result in an average angular velocity of 1.99 * 10^-7 rads/sec.

It is important to pay attention to the units when performing calculations, as they can greatly affect the final answer. Additionally, make sure to use the correct values for the time and delta theta in your calculations.

If you are still having trouble with the homework program, it may be helpful to consult with your instructor or a tutor for clarification on the correct values and units to use in the calculations.