What is the moment of inertia for a spherical shell?
The moment of inertia of spherical shell about its centroidal axis is 32MR2. Thus using parallel axis theorem we get the moment of inertia about a tangent axis is 32MR2+MR2=35MR2.
What is the moment of inertia of a solid sphere about its diameter and tangent?
Moment of inertia of solid sphere with respect to tangent touching to its surface=I′=ICM+Mr2=52MR2+M(R)2=57MR2.
What is the moment of inertia of solid sphere of density and radius about its diameter?
Solution : Moment of inertia of solid sphere about its diameter, `I=(2)/(5)MR^(2)=(2)/(5)[(4)/(3)piR^(2)rho]R^(2)=(176)/(105)rhoR^(5)`.
Why moment of inertia of solid sphere is less than spherical shell?
For a hollow cylinder all the particles are at a distance of R from the axis and hence have the same contribution to moment of inertia. However for a solid sphere some of the particles are at a distance less than R and hence their contribution to the moment of inertia is less.
What is the moment of inertia of earth about its diameter?
Therefore, moment of inertia of the earth about its diameter is 1.638×10^38 kgm².
What is the moment of inertia of a uniform disc about the diameter?
For a uniform circular disc the moment of inertia about its diameter is `150gcm^(2)`.
What is the moment of inertia of a disc about its diameter?
Thus the moment of inertia of a disc about any of its diameter is MR2/4.
What is expression for MI of solid sphere about its diameter?
Hint: Moment of Inertia (M.I.) of the solid sphere along its diameter is $I = \dfrac{{2M{R^2}}}{5}$.
What is the momentum of inertia of solid sphere of density?
dm = ρ dV, where ρ is the density of the solid cylinder and dV is the volume.
What is the moment of inertia of a circular wire of mass M and radius R about its diameter?
MR2/4.
Why the moment of inertia of the solid sphere is less than that of the spherical shell with the same radius and the same mass?
For a hollow cylinder all the particles are at the same distance from the axis and hence have the same contribution to moment of inertia. 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.
What is the moment of inertia of earth about its diameter taking it to be a sphere of radius 6400 km and mass 6 into 10 to the power 24 kg?
What is the moment of inertia of Earth about its axis of rotation?
The moment if inertia of the earth about its axis of rotation is `9.83 xx 10^37 kgm^2` and if its angular velocity is `7.3 xx 10^-5 rad s^-1`.
What is the moment of inertia of a uniform circular disc of radius R?
Solution : ( c) The moment of inertia about an axis passing through centre of mass of disc and perpendicular to its plane is `I_(CM) = (1)/(2) MR^2` where `M` is the mass of disc and `R` its radius According to theorem of parallel axis.
What is the inertia of a sphere?
Moment of inertia of sphere is normally expressed as; I = (⅖ )MR2. Here, R and M are the radius and mass of the sphere respectively.
What is the formula of moment of inertia of a solid sphere of radius R about its diameter?
Solution : `I = (2)/(5) MR^(2)`, where `M` is the mass and `R` is radius of the solid sphere.
What is the moment of inertia of circular wire about its diameter?
What is moment of inertia of circular wire of mass?
Answer. Moment of inertia of a circular wire about its axis is MR2. For finding moment of inertia around its diameter, you have to use perpendicular axis theorem. Considering its two diameters that are perpendicular to the axis. I + I = MR2.