What is the moment of inertia of a hollow sphere and a solid sphere?
where I is the Moment of Inertia, m is point mass, r is the perpendicular distance from the axis of rotation….Detailed Solution.
| Shape | Axis of rotation | Moment of inertia |
|---|---|---|
| Solid sphere | through center | I = 2 5 m r 2 |
| Hollow sphere | through center | I = 2 3 m r 2 |
What is the moment of inertia of thin spherical shell about any diameter?
The moment of inertia of a thin spherical shell of mass M and radius R about a diameter is 32MR2.
What is the moment of inertia of hollow sphere passing through the Centre and tangent to its surface?
From parallel axis theorem, Moment of inertia of solid sphere with respect to tangent touching to its surface=I′=ICM+Mr2=52MR2+M(R)2=57MR2.
Is moment of inertia of hollow bodies higher than moment of inertia of solid bodies?
If the mass and the shape are equal, the moment of inertia is proportional to the square of the diameter. A hollow body has a greater moment of inertia than a solid body with the same mass and dimensions.
What is the unit of moment of inertia?
kilogram-metre square
The unit of moment of inertia is a composite unit of measure. In the International System (SI), m is expressed in kilograms and r in metres, with I (moment of inertia) having the dimension kilogram-metre square.
What is the moment of inertia of a spherical shell?
The moment of inertia of spherical shell about its centroidal axis is 32MR2.
What is the moment of inertia of hollow sphere about it’s tangential axis?
Hence the moment of inertia of the hollow sphere about the tangential axis is given as $ \dfrac{7}{3}M{R^2} $. Note: The parallel axis theorem is also used for the rigid body by considering its inertia at a parallel axis and the perpendicular distance from the centre of the rigid mass.
What is the moment of inertia formula of a hollow center with axis through the center?
I=23MR2, where M is the mass and R is radius of the hollow sphere.
How do you determine the moment of inertia?
Calculation of Moment of Inertia. Consider a uniform rod of mass M and length L and the moment of inertia should be calculated about the bisector AB.
How to calculate moment of inertia?
Identify simply shaped subareas the composite area can be decomposed to.
What is the formula for the moment of inertia?
Simple Examples of Moment of Inertia. How difficult is it to rotate a particular object (move it in a circular pattern relative to a pivot point)?
What is the inertia of a sphere?
the moment of inertia of a solid sphere is I(solid sphere) = kg m2 and the moment of inertia of a thin spherical shell is I(spherical shell) = kg m2 Show development of expressions Index Moment of inertia concepts