Inertia and Density question help

In summary, the conversation discusses the possibility of determining the unique density distribution of the Earth based on its mass, radius, and moment of inertia. It is suggested that the solution may not be unique due to the lack of equations and the complexity of the Earth's composition. The conversation also touches on the methods of measuring the Earth's moment of inertia and the potential challenges in doing so.
  • #1
SWiTCHRiDE
7
0
Assuming I have the mass, radius and moment of inertia of the earth, is it possible to determine the unique density distribution of the earth? The assumtion is the Earth is composed of N shells with constant density and thickness.

I don't think so, but I am not sure why or how...other than the uniform density can be calculated.

thanks
 
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  • #2
I don't think the solution is unique. There may be many radial density distributions with identical moments of intertia
 
  • #3
Well, you have 2N densities&thicknesses, and three equations as far as I can see:
1. The sum of the shell's masses equals the known mass
2. The sum of the thicknesses equals the radius
3. the sum of the moments of inertae equals the Earth's moment of inertia.

looks like a typical lack of equations to me, even for N=2! :smile:
 
  • #4
SWiTCHRiDE said:
Assuming I have the mass, radius and moment of inertia of the earth
Hmm.. the radius of the Earth has long been measured, and its mass can be determined in a laboratory, but I thought the composition of the Earth was inferred from seismology - and moment of inertia perhaps from that. Of course, I wouldn't be wondering this is you wanted to calculate the density distribution of a golf ball, but is there a method of directly measuring the Earth's moment of inertia? Can you get it from simple observations of the moon and the lengthening day?
 

1. What is inertia and how does it relate to density?

Inertia is a property of matter that describes its resistance to change in motion. Density, on the other hand, is a measure of how closely packed the particles of a substance are. The more dense a substance is, the greater its inertia will be, meaning it will be harder to change its state of motion.

2. How does an object's shape affect its inertia?

The shape of an object does not directly affect its inertia. However, the distribution of mass within an object can impact its inertia. For example, an object with more mass concentrated towards its edges will have a greater rotational inertia than an object with the same mass but evenly distributed.

3. What is the relationship between inertia and Newton's First Law of Motion?

Newton's First Law of Motion states that an object will remain at rest or in motion with a constant velocity unless acted upon by an external force. Inertia is directly related to this law as it describes the tendency of an object to resist changes in its motion. In other words, an object's inertia is what causes it to continue moving or stay at rest unless acted upon by a force.

4. How does density affect an object's buoyancy?

The density of an object determines whether it will float or sink in a fluid. If the object's density is greater than the fluid it is placed in, it will sink. If the object's density is less than the fluid, it will float. This is due to the concept of buoyancy, which is the upward force exerted on an object by a fluid. Objects with a lower density will experience a greater buoyant force, causing them to float.

5. How do inertia and density play a role in understanding the motion of objects in space?

In space, objects experience minimal external forces, so their motion is primarily influenced by their inertia and density. The greater the object's mass and density, the more inertia it will have and the harder it will be to change its motion. This is why smaller objects, such as astronauts, can easily maneuver in space compared to larger objects like spaceships. Understanding the relationship between inertia and density is crucial in predicting and controlling the motion of objects in space.

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