What is the moment of inertia of a disc about | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The moment of inertia of a disc about an axis passing through its centre and perpendicular to its plane is $I_z = \frac{MR^2}{2}$,where $M$ is the

Vedclass · Accepted Answer

$ \frac{MR^2}{4} $

Vedclass · Answer

(B) The moment of inertia of a disc about an axis passing through its centre and perpendicular to its plane is $I_z = \frac{MR^2}{2}$,where $M$ is the mass and $R$ is the radius of the disc.Since the disc is a planar body,we can apply the theorem of perpendicular axes.Let the $x$ and $y$ axes lie in the plane of the disc,intersecting at the centre $O$. These axes represent two diameters of the disc.According to the theorem of perpendicular axes,$I_z = I_x + I_y$.Due to the rotational symmetry of the disc,the moment of inertia about any diameter is the same,so $I_x = I_y = I_d$.Substituting this into the theorem,we get $I_z = I_d + I_d = 2I_d$.Therefore,$I_d = \frac{I_z}{2} = \frac{1}{2} \left( \frac{MR^2}{2} \right) = \frac{MR^2}{4}$.Thus,the moment of inertia of a disc about one of its diameters is $\frac{MR^2}{4}$.

What is the moment of inertia of a disc about one of its diameters?

Similar Questions

Three identical thin rods,each of length $l$ and mass $M$,are joined together to form the letter $H$. What is the moment of inertia of the system about one of the vertical sides of the $H$?

What is the moment of inertia of a ring of mass $M$ and radius $R$ about a tangent to the circle of the ring in its own plane?

From a circular disc of radius $R$ and mass $9M$,a small disc of radius $\frac{R}{3}$ is removed concentrically. If the mass of the removed disc is $M$,what is the moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre?

The moment of inertia of a rod of length $l$ about an axis passing through its centre of mass and perpendicular to the rod is $I$. The moment of inertia of a hexagonal shape formed by six such rods,about an axis passing through its centre of mass and perpendicular to its plane,will be (in $I$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module