Angular Velocity of the Spinning Earth!

[Mr. Sinister]

1. The problem statement, all variables and given/known data
The angular velocity of the spinning earth is approximately......
0.26 rad/hr
6.28 rad/hr
0.13 rad/hr
or none of the above
I am new at this forum as of today! I hope that somebody could show me how I should even begin this! I have no idea!

2. Relevant equations
1 rev/s= 2pi rad/s


3. The attempt at a solution

[hage567]

How long does it take the earth to make 1 revolution?

[Mr. Sinister]

It should be 365 days.

[Mr. Sinister]

Wait that's around the sun.

[hage567]

How many hours are in a day?

[Mr. Sinister]

24 hours in a day.

[hage567]

OK, you've already stated how many radians are in 1 revolution. So what do you think you should do now? What's angular velocity mean?

[Mr. Sinister]

It is the rate of change of angular position. So...... The rate of change must be hmmm... I thought I had it.

[Mr. Sinister]

Could the position be 1 revolution and the rate of change 24hrs.?

[hage567]

Could the position be 1 revolution and the rate of change 24hrs.?

Yes, you know it goes through 1 revolution in 24 hrs.

[Mr. Sinister]

Do I put those numbers into an equation?

[hage567]

Well yes you could do it that way. \omega = \frac{\Delta\theta}{\Delta t}

revolutions/hr is a way of stating angular velocity. Look at the units the answers are given in. What do you need to do to get those?

[Mr. Sinister]

Well, I believe that there is 2pi radians in a circle. That equation is the change in the angle over the change in time right? I don't know if this info even helped me?

[Mr. Sinister]

I am very grateful for your help! This is great considering the tutor room where I go on campus is insanely full with only one tutor per 30 students!

[hage567]

Yes there are 2pi radians in a one revolution. The answer is asking for units of radians/hr. You now have everything you need. Your angular velocity is then going to be (2*pi radians)/(24 hrs) which is the change in angle over time, like you say. So what number do you get when you put that into your calculator?

[hage567]

I am very grateful for your help! This is great considering the tutor room where I go on campus is insanely full with only one tutor per 30 students!

You're welcome. Hopefully I'm being helpful.

[Mr. Sinister]

.26 rad/hr! Thanks!

[Mr. Sinister]

You were very helpful! Do you get paid for helping people? Or is it out of pure kindness? I've noticed that there is alot of homework helpers in the staff section.

[hage567]

I'm glad I could help. We do this on our own time for fun. :biggrin:

[Mr. Sinister]

Wow!!! That's Awesome!!! Thanks Again!!! I'll be back for sure at a later day!!!