Total Angular Momentum of the Earth

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Homework Help Overview

The discussion revolves around determining the period of Earth's rotation such that its total angular momentum, which includes both its rotation about its axis and its orbit around the sun, equals zero. The problem involves concepts from angular momentum and motion in physics.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the relationship between translational and rotational angular momentum, questioning the setup of equations and the definitions of variables involved. There are attempts to equate the two forms of angular momentum and clarify the variables used in the equations.

Discussion Status

Some participants have provided guidance on checking equations and clarifying variable definitions. There is an ongoing exploration of how to isolate the period of rotation and the implications of using different variables for radius in the context of angular momentum.

Contextual Notes

Participants note potential confusion regarding the definitions of variables and the need to distinguish between different radii in the equations. The problem is framed within the constraints of a homework assignment, emphasizing the importance of understanding the underlying physics rather than simply finding a solution.

v3r
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Homework Statement


How long should the day be so that the total angular momentum of the Earth
(including its rotation about its own axis and its (approximately) circular orbit around the
sun) is zero (Note: the magnitude of the angular velocity is 2pi/T where T is the period of rotation?)

Homework Equations


Ltot = Ltrans + Lrot
Lrot = Iw^2
w = 2pi/T

The Attempt at a Solution


Ltot = 0

I am really clueless. I don't know where to start..
 
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v3r said:

Homework Statement


How long should the day be so that the total angular momentum of the Earth
(including its rotation about its own axis and its (approximately) circular orbit around the
sun) is zero (Note: the magnitude of the angular velocity is 2pi/T where T is the period of rotation?)

Homework Equations


Ltot = Ltrans + Lrot
Lrot = Iw^2
w = 2pi/T

The Attempt at a Solution


Ltot = 0

I am really clueless. I don't know where to start..

you're started. double check your equation
Lrot = Iw^2

There shouldn't be a square there. For the Earth's orbital angular momentum, just treat the Earth like a point mass at a distance r.

L=mvr
 
So it should be
Ltot = Ltrans + Lrot
Ltot = 0
Ltrans = Lrot
mvr = Iw
mvr = 2pi/T * I
mvr = 2pi/T * mr^2
v/r = 2pi/T

I'm still confused.
 
v3r said:
So it should be
Ltot = Ltrans + Lrot
Ltot = 0
Ltrans = Lrot
mvr = Iw
mvr = 2pi/T * I
mvr = 2pi/T * mr^2
v/r = 2pi/T

I'm still confused.

You're getting there. Remember, you're looking for the period of one day on Earth under your new conditions. what variable do you want to solve for?

Also, be carefull with your variables. You've used "r" to stand in for two different things.

What is the r in Ltrans = mvr?
What is the r in I = mr^2?
 
r in I would be the perpendicular distance which would be the radius of the earth.
r in Ltrans would be the distance to the center of mass which would be the distance of Earth from sun?

I want to solve for v in order to get the time by dividing it by the radius?
 
You're almost there. Now use another variable to re-name one of your r's. Eventually, you want to solve for period T. However, you have the Earth's orbital velocity v to get rid of. For this, use univorm circular motion, and universal gravitation.

F=m(v^2) / rF=GmM / (r^2)
 

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