How Does Angular Momentum Affect Local Spacetime Curvature?

In summary, the conversation discusses the relationship between angular momentum and momentum, as well as the effects of gravity and spacetime curvature on an ice skater's rotation. It also raises the question of why other objects are not affected by the strong curvature of spacetime near the ice skater.
  • #1
rlance
1
0

Homework Statement



t seems to me all momentum is angular momentum. An ice skater pulling in her arms will rotate faster, and obversely, extending her arms will slow her rotation. If her arms are extended to the radius of the planet, her rate of spin will slow to unnoticeable (to us), seeming instead to go in a straight line.

If as Einstein concluded, gravity and acceleration are indistinguishable, the spacetime curvature shown as gravity ought also to be observed as we shorten the arms of the ice skater from 4000 miles to 1 meter. She spins faster, and has a correspondingly more curved signature in her local spacetime.

So why aren’t other things close to her “sucked in” to her much more curved spacetime?

Homework Equations







The Attempt at a Solution

 
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  • #2
How do you know they are not?
Do the math and see.
 

FAQ: How Does Angular Momentum Affect Local Spacetime Curvature?

What is angular momentum?

Angular momentum is a measure of the rotational motion of an object around an axis. It is a vector quantity that is dependent on an object's mass, velocity, and distance from the axis of rotation.

How does angular momentum affect objects in orbit?

Angular momentum is conserved in a closed system, meaning that as an object in orbit moves closer or further away from its axis of rotation, its angular momentum will remain constant. This is why planets in our solar system maintain their orbits around the sun.

What is the relationship between angular momentum and gravity?

Angular momentum and gravity are related through the law of gravitation, which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This force affects the angular momentum of an orbiting object, keeping it in its orbital path.

Can angular momentum be changed?

Yes, angular momentum can be changed if an external force or torque is applied to an object. For example, a spinning top will continue to spin on its axis until an external force (such as friction) slows it down or changes its direction.

How is angular momentum used in physics and engineering?

Angular momentum is used in numerous applications, including understanding the movements of celestial bodies, designing satellites and spacecraft, and analyzing the behavior of spinning objects such as tops and gyroscopes. It is also a key concept in the field of quantum mechanics.

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