Question about angular momentum?

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To calculate the angular momentum of the Earth system, one should use the formula L = I ω for its rotation about its axis, where I is the rotational inertia and ω is the angular velocity. For the Earth's orbital angular momentum around the sun, the formula L = MV x R can be applied, with M being the mass and V the orbital velocity, which is approximately 30 km/s, not 3 km/s. It's important to note that angular momentum is conserved unless acted upon by an external torque; internal torques, such as pushing walls, do not change it. To find the total angular momentum of the Earth, both its rotation and orbital motion must be considered. Understanding these concepts is crucial for accurately determining the angular momentum of the Earth system.
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"
 
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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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