Angular Velocity of the Spinning Earth

[Mr. Sinister]

Homework Statement

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!

Homework Equations

1 rev/s= 2pi rad/s

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 a lot of homework helpers in the staff section.

 

[hage567]

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

 

[Mr. Sinister]

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