Does diameter affect moment of inertia?
Table of Contents
- 1 Does diameter affect moment of inertia?
- 2 What is the moment of inertia for a hollow cylinder?
- 3 Why does a hollow cylinder have a high moment of inertia?
- 4 What affects moment of inertia?
- 5 Would you expect the moment of inertia of a sphere to be greater than or less than the moment of inertia of a cylinder with the same radius and total mass?
- 6 What are the different factors on which moment of inertia depends?
Does diameter affect moment of inertia?
Moment of inertia is directly proportional to the square of the radius.
What is the moment of inertia for a hollow cylinder?
HOLLOW CYLINDER MOMENT OF INERTIA
| Moment of Inertia of Hollow Cylinder Formula | |
|---|---|
| Mass moment of inertia about x axis | Ix= (m/12) * (3*(R22+R12) + h2) |
| Mass moment of inertia about y axis | Iy= (m/12) * (3*(R22+R12) + h2) |
| Mass moment of inertia about z axis | Iz= (m/2) * (R12+R22) |
Why does a hollow cylinder have a high moment of inertia?
For a given mass, a hollow cylinder has more material away from the axis than a solid cylinder, so its moment of inertia is higher. This means that more of the potential energy is being turned into spinning the cylinder, so less is left over for the translational KE.
Why hollow cylinder with the same mass has high moment of inertia than solid cylinder?
So, since the hollow cylinder has all it’s mass at the border in comparison with the solid one which distributes all it’s mass from the center (with very small contribution) to the border, it has a higher moment of inertia and thus more rotational energy.
Does moment of inertia depend on shape?
Angular velocity. Hint: Moment of Inertia is a rotational analogue for mass. The moment of inertia is proportional and depends upon the mass distribution, axis of rotation and the shape of the object. Also, Moment of inertia varies with the shape of the object.
What affects moment of inertia?
The moment of inertia of an object usually depends on the direction of the axis, and always depends on the perpendicular distance from the axis to the object’s centre of mass.
Would you expect the moment of inertia of a sphere to be greater than or less than the moment of inertia of a cylinder with the same radius and total mass?
On the other hand, for a solid sphere some particles are at different distance from other, thus their contribution to the moment of inertia is less. So the overall moment of inertia of a solid sphere is less than a hollow cylinder.
What are the different factors on which moment of inertia depends?
The moment of inertia of a body depends on the following factors: i Mass of the body. ii Size and shape of the body. iii Distribution of mass about the axis of rotation. iv Position and orientation of the axis of rotation with respect to the body.
What are two factors on which moment of inertia depends?
The moment of inertia depends on the following factors,
- The density of the material.
- Shape and size of the body.
- Axis of rotation (distribution of mass relative to the axis)