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Za Kh
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I know the moment of inertia for both a solid sphere and a hollow sphere is , but my teacher has derived a moment of inertia of the sphere but am not sure about what axis she was deriving it , and she got this answer 3/5 MR^2
I also think that there must be a mistake in her derivation. Do you have it? Do you agree with all the steps?Za Kh said:I know the moment of inertia for both a solid sphere and a hollow sphere is , but my teacher has derived a moment of inertia of the sphere but am not sure about what axis she was deriving it , and she got this answer 3/5 MR^2
Oh! It is clearly wrong. I hope a teacher did not do that in a class!Replusz said:Was she doing this?
http://imgur.com/dc0ZTvG
But what does that mean exactly? There is no way to make a sphere rotate in such a way that it will have that moment of inertia, so it is actually a completely unphysical result. That's why it is never quoted as a moment of inertia of a sphere.Za Kh said:Now I understand , it has turned out that she meant the moment of inertia of the center of sphere and I thought it were the moment of an axis passing through the center , just because she hasn't specified clearly what she meant , thank you everyone :)
Do you mean a hemisphere? Solid or hollow?Za Kh said:How could we calculate the moment of inertia of a sphere , cut into half by the xoy plane
The "xy" axis is a synonym for an axis in the z direction? So if the moment of inertia about this axis is zero, every point within the sphere must be somewhere on the z axis.Za Kh said:How could we calculate the moment of inertia of a sphere , cut into half by the xoy plane ,, its supposed that moment of ineria about the xy and zy axes is zero , i want to know why
A solid spherecnh1995 said:Do you mean a hemisphere? Solid or hollow?
They are not given zero to us , they should be proved by calculation , but am not knowing howjbriggs444 said:The "xy" axis is a synonym for an axis in the z direction? So if the moment of inertia about this axis is zero, every point within the sphere must be somewhere on the z axis.
The "zy" axis is a synonym for an axis in the x direction? So if the moment of inertia about this axis is zero, every point within the sphere must be somewhere on the x axis.
It follows that every point within the sphere must be at the intersection of the x and z axes. i.e. at the origin. Well, yeah, that moment of inertia is fairly easy to calculate.
The moment of inertia of a sphere is a measure of its resistance to rotational motion. It is the rotational analog of mass in linear motion, and is determined by the distribution of mass within the sphere and its distance from the axis of rotation.
The moment of inertia of a sphere can be calculated using the formula I = (2/5)mr^2, where m is the mass of the sphere and r is the radius. This formula is derived from the integration of infinitesimal elements of mass within the sphere.
The moment of inertia of a sphere is affected by its mass and radius, as well as the distribution of mass within the sphere. A larger mass or radius will result in a larger moment of inertia, while a more spread out mass distribution will decrease the moment of inertia.
Moment of inertia plays a crucial role in rotational dynamics, as it determines how much torque is required to accelerate a sphere into rotational motion. It is also used in the calculation of angular momentum and the conservation of angular momentum in various physical systems.
The moment of inertia of a sphere is the lowest of all solid shapes with the same mass and radius. This means that a sphere requires the least amount of torque to start rotating compared to other shapes. For example, a solid cylinder with the same mass and radius as a sphere would have a moment of inertia that is 1.5 times greater.