Parallel Axis Theorem?
Suppose a uniform slender rod has a length ( L ) and a mass ( m ). The moment of inertia of the rod about an axis that is perpendicular to the rod and passes through its center of mass is given by ( I_{cm} = \frac{1}{12} m L^2 ). Using the Parallel Axis Theorem, find ( I_{\text{end}} ), the moment of inertia of the rod with respect to a parallel axis that passes through one end of the rod. Express ( I_{\text{end}} ) in terms of ( m ) and ( L ).
4 Answers
Dec 30, 2024
Parallel axis theorem:
Moment of inertia about arbitrary axis
=
Moment of inertia about center of mass
+
(mass)(distance between cm and axis)^2
They give you the moment about CM (or you can look it up)
then just add (m)(L/2)^2 to that.
The M.I of a cube about an axis passing through the center of any two faces is
ma² / 6 where a is the side of the cube and m is the mass of the cube.
An edge of the cube is at a distance of (√2) / 2 of the side a .
By parallel axis theorm
The M.I about the edge of the cube is ma² / 6 + m [(√2)a / 2] ² = (2/3) ma ²
To make it easier, you add the equation they gave you, which for me was (1/12)m(L^2) and add it to (m)(L/2)^2. This results in (1/3)m(L^2)
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