Question
Download Solution PDFThe moment of inertia of a solid cone of mass m and base radius r about its vertical axis is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Moment of Inertia
- The moment of inertia of a rigid body about a fixed axis is defined as the sum of the product of the masses of the particles constituting the body and the square of their respective distances from the axis of the rotation.
- The moment of inertia of a body is given by
I = m R2
where m = Mass and R = Distance from the axis
The moment of inertia of a solid cone
m is the mass of the cone and r is the base radius of the cone and h is the height of the cone.
About the vertical axis
\(I_z={3\over 10}mr^2\)
Additional Information
About an axis passing through the tip:
\(I_x=I_y=m({{3\over20}r^2+{3\over5}h^2})\)
About an axis passing through the base along diameter:
\(I_x=I_y=m({{3\over20}r^2+{1\over10}h^2})\)
About a horizontal axis passing through the centre of mass:
\(I_x=I_y=m({{3\over20}r^2+{3\over80}h^2})\)
Last updated on May 30, 2025
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