Question about angular momentum?

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Discussion Overview

The discussion revolves around calculating the angular momentum of the Earth system, exploring different aspects such as its rotation about its axis and its orbit around the sun. Participants consider various formulas and concepts related to angular momentum, including the effects of internal and external torques.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant proposes using the formula L = MV x R for calculating angular momentum, questioning whether to use Earth's angular velocity or its orbital velocity around the sun.
  • Another participant clarifies that angular momentum is defined as L = Mv x R, noting that angular velocity (w) and linear velocity (v) are not the same.
  • A participant corrects the orbital speed of the Earth, stating it is approximately 30 km/s, not 3 km/s.
  • One participant suggests using the formula L = I ω for calculating the Earth's angular momentum due to its rotation, where I is the rotational inertia and ω is the angular velocity.
  • There is a question about whether to consider both the Earth's orbital motion and its rotation when calculating total angular momentum.
  • Another participant agrees that both rates need to be considered for total angular momentum but notes that for orbital angular momentum alone, the Earth's rotation can be ignored.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate formulas and considerations for calculating angular momentum, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

Participants discuss various formulas and their applicability, highlighting the complexity of calculating angular momentum in different contexts. There are unresolved assumptions regarding the definitions and conditions under which these formulas apply.

zeromodz
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Okay, say I wanted to know the angular momentum of the Earth system.

L = MV x R

Would I use Earth's angular velocity instead of its 3km/s velocity around the sun?

Then, wouldn't the formula be?

L = MW x R

I am just trying to find the angular momentum in the Earth system. Also, is it conserved even though we can put a torque on it just by pushing walls around connected to the earth?

Thanks.
 
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angular momentum is defined as

L = Mv x R

w and v are not the same.

v = w x RL can change only with an external torque. If you push the walls (or even a mountain), the torque is internal and would not cause L to change.
 
The Earth moves at about 30km/s around the sun.Not 3km/s.
TM
 
zeromodz said:
Okay, say I wanted to know the angular momentum of the Earth system.

L = MV x R

Would I use Earth's angular velocity instead of its 3km/s velocity around the sun?

Then, wouldn't the formula be?

L = MW x R

I am just trying to find the angular momentum in the Earth system. Also, is it conserved even though we can put a torque on it just by pushing walls around connected to the earth?

Thanks.
If you wanted to find the Earth's angular momentum due to its rotational about its axis, a better formula would be:
L = I ω, where I is the Earth's rotational inertia and ω is its angular velocity.

The formula L = r X MV is useful for a point mass. Note that each part of the Earth is a different distance (r) from the axis and has a different tangential speed (V).

See: http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html"

Compared with: http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html#am"
 
Last edited by a moderator:
What would you do if you wanted to find the angular momentum of the Earth around the sun? Would you need to consider both the rate at which the Earth orbits the sun and the rate at which the Earth spins around its own axis?
 
Yaridovich said:
What would you do if you wanted to find the angular momentum of the Earth around the sun? Would you need to consider both the rate at which the Earth orbits the sun and the rate at which the Earth spins around its own axis?
Yes, if you wanted the total angular momentum. If all you cared about was the orbital angular momentum, you could ignore the Earth's rotation.
 

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