Calculating Angular Velocity: Earth's Rotation & Orbital Speed

[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?

 

[Andrew Mason]

What are the questions?

AM

 

[kerimek]

Hello,

Thank you for sharing your calculations and questions. It seems like you have a good understanding of the concepts of angular velocity and how to calculate it. However, there are a few things that may have caused the discrepancy in your answers.

Firstly, for the Earth's rotation, you correctly used the formula Wavg = Delta Theta / Delta Time, but it seems like you may have used the wrong value for delta time. The time it takes for the Earth to rotate once on its axis is not exactly 84600 seconds, but rather 23 hours, 56 minutes, and 4.1 seconds. This is known as a sidereal day, and it is slightly shorter than a solar day, which is the time it takes for the sun to appear in the same position in the sky. Using the correct value for delta time should give you a more accurate answer for the Earth's rotational angular velocity.

For the Earth's orbital speed around the sun, you may have used the wrong value for delta theta. The Earth's orbital motion is not a complete circle, but rather an elliptical path. Therefore, the delta theta would not be exactly 2 Pi radians. Instead, it would be the angle swept out by the Earth in one year, which is approximately 2 Pi radians for small angles. Using the correct value for delta theta should give you a more accurate answer for the Earth's orbital angular velocity.

I hope this helps clarify the issue and helps you get the correct answers. Remember to always double-check your values and units to ensure accuracy in your calculations. Keep up the good work!