Angular velocity Homework help

[physics1331]

Homework Statement

"Many rivers, like hte Mississippi River, flow from north to south toward the equator. These rivers often carry a large amount of sediment that they deposit when entering the ocean. What effect does this redistribution of material have on the angular velocity of the earth? Why?"

"A person is hanging motionless from a vertical rope over a swimming pool. She let's go of the rope drops straight down. After letting go, is it possible for her to curl into a ball and start spinning? Justify your answer."


Thanks

Homework Equations

The Attempt at a Solution

First, I am guessing that the question refers to the Earth rotating about its axis, not revolving around the sun. If I am right on that part, would the effect be that it slows the angular velocity? The only reason I think that is the mass is moving farther away from the axis of rotation.

My guess is no because initially she has no angular velocity, meaning that she has not angular momentem. Thus, even if the moment of inertia changes, she will still have zero angular momentum.

 

[Gokul43201]

Correct, on both. For the first one, you might want to specifically mention the effect on the moment of inertia.

 

[m2003]

Therefore, she cannot start spinning.

Hello,

Your understanding of the first question is correct. The redistribution of sediment from rivers into the ocean does indeed have an effect on the Earth's angular velocity. This is due to the conservation of angular momentum, which states that the total angular momentum of a system remains constant unless acted upon by an external torque. In this case, the rivers are depositing sediment into the ocean, which changes the distribution of mass on the Earth's surface. This changes the moment of inertia of the Earth, which in turn affects its angular velocity. As the moment of inertia increases, the angular velocity decreases, and vice versa.

As for the second question, you are correct that the person cannot start spinning after letting go of the rope. This is because, as you mentioned, they have no initial angular velocity or angular momentum. Even if they were to curl into a ball, the moment of inertia would decrease, but without any external torque acting on them, they would not start spinning. Angular momentum must be conserved in this scenario.

I hope this helps clarify the concepts of angular velocity and angular momentum for you. Let me know if you have any further questions. Good luck with your homework!