Angular Displacement: Earth's Orbit 2 Days

In summary, during its orbit around the sun, Earth rotates 2π/365.25 radians in 1 day and 0.0344048476 radians in 2 days. To find the change in velocity, the angular velocity (ω) can be calculated using the change in angular displacement and time, and then multiplied by the distance from the center of rotation (r) to find the linear velocity (v). The relationship between v, ω and r is v=rω.
  • #1
salaam
18
0

Homework Statement



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?

Homework Equations



Theta=Theta final - Theta inital

The Attempt at a Solution



I'm very confused and need help starting it!
 
Physics news on Phys.org
  • #2
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
salaam said:

Homework Statement



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?

Homework Equations



Theta=Theta final - Theta inital

The Attempt at a Solution



I'm very confused and need help starting it!

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
2 pi i think
 
  • #5
salaam said:
2 pi i think

Right right good good...


so if in 365.25 days it rotates 2pi radians

in 1 day how much will it rotate?
 
  • #6
(2 * pi radians) / 365.25 = 0.0172024238
 
  • #7
salaam said:
(2 * pi radians) / 365.25 = 0.0172024238

good good

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

So in 2 days how much does it rotate?
 
  • #8
0.0344048476 radians
 
  • #9
salaam said:
0.0344048476 radians

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
YES! thank you so much for your help :)
 
  • #11
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
salaam said:
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

Well you know 2 days it rotates 0.0344048476 radians

the angular velocity ω is defined as d/dt or

[tex]\omega = \frac{\theta_2 - \theta_1}{t} = \frac{change \ in \ angular \ displacement}{time}[/tex]


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

So in 2 days what is ω ?
 
  • #13
.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
salaam said:
.0172 radians/ days.. but its not asking for angular velocity so it doesn't want my answers in radians/ days or hours or seconds

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
i converted w to radians/ second and got. 1.99 x 10^-7. i have no idea what the relationship is
 
  • #16
salaam said:
i converted w to radians/ second and got. 1.99 x 10^-7. i have no idea what the relationship is

So you know the equation v=rω?
 
  • #17
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
salaam said:
OHH so i would just do v= 6378 km ( 1.99 x 10^-7) and that would give me my answer in km/second?

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
OHH so i just do v= 6378 km ( 1.99 x 10 ^-7) and my answer comes out in km/s?
 
  • #20
salaam said:
OHH so i just do v= 6378 km ( 1.99 x 10 ^-7) and my answer comes out in km/s?

uhm yes basically.
 

1. What is angular displacement?

Angular displacement is the change in the angle of an object's position, measured from a reference point. It is typically expressed in degrees or radians.

2. How does Earth's orbit cause angular displacement?

Earth's orbit around the sun causes it to constantly change its position in relation to other celestial bodies. This change in position results in angular displacement, as the angle between Earth's position and the reference point (such as the vernal equinox) changes over time.

3. Can angular displacement be negative?

Yes, angular displacement can be negative. It depends on the direction of the movement and the chosen reference point. A negative angular displacement means that the object has moved clockwise from its original position.

4. How is angular displacement different from linear displacement?

Angular displacement measures the change in angle, while linear displacement measures the change in distance. Angular displacement is a rotation around a fixed point, while linear displacement is a straight line movement from one point to another.

5. Why is angular displacement important in studying Earth's orbit?

Angular displacement is important in studying Earth's orbit because it helps us understand the movement of the Earth in relation to the sun and other celestial bodies. It also allows us to predict when certain astronomical events, such as equinoxes and solstices, will occur.

Similar threads

  • Introductory Physics Homework Help
Replies
15
Views
4K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
608
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
14
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
5K
  • Introductory Physics Homework Help
Replies
2
Views
2K
Back
Top