Questions and Answers
What is the formula for calculating the moment of inertia of an irregular body?
I = ∫r^2 dm
How does the distribution of mass affect the moment of inertia of an irregular body?
Mass concentrated closer to the axis decreases the moment of inertia
What is the unit of moment of inertia?
kg m^2
Study Notes
Moment of Inertia of Irregular Bodies
- The moment of inertia of an irregular body can be calculated using the formula: I = ∫r^2 dm, where I is the moment of inertia, r is the distance from the axis of rotation, and dm is the mass of a small element of the body.
- The distribution of mass in an irregular body affects its moment of inertia, with mass concentrated closer to the axis of rotation resulting in a lower moment of inertia and mass distributed farther away from the axis resulting in a higher moment of inertia.
- The unit of moment of inertia is typically kg·m^2 or other units of mass multiplied by units of distance squared.
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