The moment of inertia of a semicircular ring | vedclass

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

Question

(A) complete circular ring of mass $M$ and radius $R$ has a moment of inertia $I = MR^2$ about an axis passing through its center and perpendicular to

Vedclass · Accepted Answer

$MR^2$

Vedclass · Answer

(A) complete circular ring of mass $M$ and radius $R$ has a moment of inertia $I = MR^2$ about an axis passing through its center and perpendicular to its plane.Since a semicircular ring is just half of a full ring,we can consider it as a system of particles where each particle is at a distance $R$ from the center.The moment of inertia is defined as $I = \sum m_i r_i^2$.For a semicircular ring,every mass element $dm$ is at a distance $R$ from the center.Therefore,$I = \int r^2 dm = \int R^2 dm = R^2 \int dm = MR^2$.Thus,the moment of inertia of a semicircular ring about an axis passing through its center and perpendicular to its plane is $MR^2$.

The moment of inertia of a semicircular ring of mass $M$ and radius $R$ about an axis passing through its center and perpendicular to its plane is:

Similar Questions

The radius of gyration of a uniform rod of length $l$ about an axis passing through a point $\frac{l}{4}$ away from the centre of the rod and perpendicular to it is:

The moment of inertia of a uniform rectangular plate about an axis passing through its center and parallel to its length $(l)$ is ($b =$ width of the rectangular plate):

Two loops $A$ and $B$ of radii $R_1$ and $R_2$ are made from a uniform wire. If the moment of inertia of $A$ is $I_A$ and that of $B$ is $I_B$,then find the ratio $R_2 / R_1$ given that $I_A / I_B = 27$.

$A$ circular disc is made using iron and aluminum such that its moment of inertia about its geometric axis is maximum. For this to happen:

If the length of a thin uniform rod is $L$ and the radius of gyration of the rod about an axis perpendicular to its length and passing through one end is $K$, then $K: L=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module