# Angular Displacement

1. Sep 26, 2009

### salaam

1. The problem statement, all variables and given/known data

Earth's orbit around the sun is nearly circular. The period is 1 yr = 365.25 days. In an elapsed time of 2.0 days, what is earth's angular displacement?

2. Relevant equations

Theta=Theta final - Theta inital

3. The attempt at a solution

I'm very confused and need help starting it!

2. Sep 26, 2009

### slider142

It stands to reason that if Earth travels 365 degrees (2Pi radians) in 365.25 days, then Earth travels ___ degrees in 2 days. You should be able to set up an algebraic equation for this one.

3. Sep 26, 2009

### rock.freak667

if period is the time taken for one revolution and it is an approximate circle. Then in 1 time period (365.25 days) how many radians does it travel?

4. Sep 26, 2009

### salaam

2 pi i think

5. Sep 26, 2009

### rock.freak667

Right right good good...

so if in 365.25 days it rotates 2pi radians

in 1 day how much will it rotate?

6. Sep 26, 2009

### salaam

(2 * pi radians) / 365.25 = 0.0172024238

7. Sep 26, 2009

### rock.freak667

good good

so in 1 day it rotates 2π/365.25 radians.

So in 2 days how much does it rotate?

8. Sep 26, 2009

### salaam

9. Sep 26, 2009

### rock.freak667

so in 2 days it rotates 0.0344048476 radians, isn't this what the question asked for ? (you can convert it degrees depending on what the question wants)

10. Sep 26, 2009

### salaam

YES! thank you so much for your help :)

11. Sep 26, 2009

### salaam

Is there anyway you can also help me find out the change in the earth's velocity? i know that velocity is change in distance over time. but it keeps telling me that i can' tput my answer in radians/seconds so i dontk now how to do it

12. Sep 26, 2009

### rock.freak667

Well you know 2 days it rotates 0.0344048476 radians

the angular velocity ω is defined as d/dt or

$$\omega = \frac{\theta_2 - \theta_1}{t} = \frac{change \ in \ angular \ displacement}{time}$$

and you have the change in angular displacement is 0.0344048476 radians.

So in 2 days what is ω ?

13. Sep 26, 2009

### salaam

.0172 radians/ days.. but its not asking for angular velocity so it doesn't want my answers in radians/ days or hours or seconds

14. Sep 26, 2009

### rock.freak667

Yes but we need ω to get v. Convert ω to radians/second.

Now what is the relationship between v, ω and r ? (r is the distance from the center of rotation -> the sun in this case)

15. Sep 26, 2009

### salaam

i converted w to radians/ second and got. 1.99 x 10^-7. i have no idea what the relationship is

16. Sep 26, 2009

### rock.freak667

So you know the equation v=rω?

17. Sep 26, 2009

### salaam

OHH so i would just do v= 6378 km ( 1.99 x 10^-7) and that would give me my answer in km/second?

18. Sep 26, 2009

### rock.freak667

Well I don't know the distance between the sun and the Earth, but that is what you would do.

Also if that is wrong, try using r=radius of sun + distance between the sun and the earth + radius of the earth. Not sure they meant to use the sun and earth as point masses or how they normally are.

19. Sep 26, 2009

### salaam

OHH so i just do v= 6378 km ( 1.99 x 10 ^-7) and my answer comes out in km/s?

20. Sep 26, 2009

### rock.freak667

uhm yes basically.