George3 said:Homework Statement
A hollow sphere has a mass of 15 kg, an inner radius of 12 cm and an outer radius of 18 cm. What is the rotational inertia (moment of inertia) of the sphere about an axis passing through its center?
Homework Equations
The Attempt at a Solution
I = 2/3 MR^2 for a hollow sphere so i did this:
2/3 (15) (.18^2) = .32 kg m^2
But this is wrong the answer is .24 kg m^2.
Any thoughts?
George3 said:BUMP... FINAL TOMORROW NEED HELP ON THIS
I really need help on this. And to the previous poster the moment of inertia of a hollow sphere is bigger than that of a solid so your method would not work...right?
AEM said:Well, I just computed your moment of inertia by doing what I told you to do and got the right answer. Your mistake is confusing a sphere with a spherical portion of the interior removed with a spherical shell.
By the way, you will have to compute the density of the material out of which the object is made.
George3 said:So did you take (2/5)MR^2 for both radii and then subtract the two moments of inertia? Which formula for I did you use??
The moment of inertia of a hollow sphere is a measure of its resistance to rotational motion. It is a mathematical property that describes how mass is distributed around the axis of rotation.
The moment of inertia of a hollow sphere can be calculated by using the formula I = (2/3)MR^2, where I is the moment of inertia, M is the mass of the sphere, and R is the radius of the sphere.
The moment of inertia of a hollow sphere is affected by its mass and radius. The larger the mass and radius, the larger the moment of inertia will be.
The moment of inertia is important because it helps to determine how an object will behave when subjected to rotational motion. It is also used in calculations for angular momentum and torque.
The moment of inertia of a hollow sphere is different from other shapes, such as a solid sphere or a cylinder. This is because the mass is distributed differently in these shapes, resulting in different moment of inertia values.