What is the moment of inertia of a uniform semicircular wire of mass m and radius r about a line perpendicular to the plane of the wire through the centre?

What is the moment of inertia of a uniform semicircular wire of mass m and radius r about a line perpendicular to the plane of the wire through the centre?

The moment of inertia of a uniform semicircular wire of mass m and radius r, about an axis passing through its centre of mass and perpendicular to its plane is mr2(-kπ2).

What is the moment of inertia of uniform semicircular wire?

The moment of inertia of a semicircular ring about a line perpendicular to the plane of the ring through its centre is given as $I=m{{r}^{2}}$, where m and r are the mass and radius of the ring. In this case, the mass of the half-ring is dm and its radius is x.

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What is the moment of inertia of semicircular disc?

Therefore, the moment of inertia of a semicircular disc of mass M and radius R about an axis passing through its centre and perpendicular to its plane is MR22.

What is the Centre of mass of a semicircular ring?

Hence, (Cx,Cy)=(0,2Rπ). Hence, the center of mass of a semi circular ring lies on the vertical passing through its center of curvature at a distance of 2Rπfrom the center of curvature.

What is the Centre of mass of a semicircular disc?

Centre of Mass is a fixed point on the object about which the entire mass of the system is equally distributed. Knowing the value of the centre of mass is useful in solving mechanics problems, where we have to describe the motion of unevenly shaped objects and complicated systems.

What is the centre of mass of ring?

The centre of mass of the ring will lie on the vertical line passing through the centre of the ring. The vertical line is considered as the y-axis. The horizontal line seen in the figure is the x-axis. We are considering an elemental mass dM on the ring.

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What is the area of circular ring?

Therefore, the area of a circular ring = π(R + r) (R – r), where R and r are the radii of the outer circle and the inner circle respectively.

What is the moment of inertia of a square plate?

m = Mass of the plate, a = Side length. In the same manner, the MOI of the square plate along the axis passing through the center and parallel to the y-axis will also be (ma2)/12. Hence, the Moment of Inertia of a square plate along the axis passing over the center and perpendicular to it will be, I [z] = (ma2)/6.