That's correct.Will said:Someone please tell me is I am doing this problem correctly.If I have a thick spherical shell with inner radius r, outer radius R, and mass M, I am getting [(2/5)M/(R^3-r^3)](R^5-r^5).
Not exactly. If you treat the hole as a sphere of negative mass, then you can subtract the rotational inertia of each sphere: [itex]I_{shell} = I_{R-sphere} - I_{r-sphere}[/itex]. But realize that the mass of each sphere is different. If you express this answer in terms of the mass of the shell instead of the mass of either sphere, then you will find that you get the same answer as above.It is not the same thing as subtracting I of large sphere from I of smaller one, different than (2/5)M(R^2-r^2)?
JohnDubYa said:I think we need to see your work. Do you know how to LaTeX your posts?
Poke around in this thread for many, many examples: https://www.physicsforums.com/showthread.php?t=8997Will said:Do you mean making my equations in "pretty print"? Please show me where I can learn to do this, its so much easier to read!
krab said:As a check, let the shell thickness approach zero to get the MI of a thin shell.
[tex]\Delta R^5/\Delta R^3=5R^4/3R^2=(5/3)R^2[/tex]
This is multiplied by [itex](2/5)M[/itex]. The result is the correct answer of
[tex](2/3)MR^2[/tex].
Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It depends on the mass and distribution of mass around the axis of rotation.
The formula for calculating the rotational inertia of a thick spherical shell is I = (2/3) * m * r^2, where I is the moment of inertia, m is the mass of the shell, and r is the radius of the shell.
Rotational inertia is a measure of an object's resistance to changes in its rotational motion, while mass is a measure of an object's resistance to changes in its linear motion. Rotational inertia takes into account the distribution of mass, while mass does not.
The thickness of a spherical shell has a direct impact on its rotational inertia. As the thickness increases, the moment of inertia also increases. This is because more mass is distributed farther from the axis of rotation, increasing the object's resistance to changes in its rotational motion.
Understanding rotational inertia of thick spherical shells is important in various engineering and physics applications. For example, it is crucial in designing and analyzing the stability and balance of rotating machinery and equipment, such as flywheels and turbines. It is also useful in sports equipment design, such as in the construction of golf clubs and baseball bats. Additionally, it is relevant in understanding the motion and stability of celestial bodies, such as planets and moons.