We can now use this information to find the balancing

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Unformatted text preview: on to find the balancing point called the center of mass. (Note: The center of mass is in a sense the average position of the mass of the lamina and may lie outside the region R) Now we will investigate the Moment of Inertia also referred to as Mass Moment of Inertia or Rotational Inertia. This is measure of an object’s RESISTANCE to changes to its rotation or how much force needs to be applied to start the object rotating (or change the rate of rotation) around some axis. We used this idea in section 11.3 but never calculated the value itself. Review of Some Formulas: Linear Dynamics F = ma KE = p = mv Rotational Dynamics For 1D we have point masses along the x-axis where our axis of rotation is at zero. The formula for the moment of inertia is: This formula can be generalized to the 2D case where we have a lamina. Summary of Section 13.2 1 Computing the Area using a double integral 2 Computing the Volume using a double integral 3 Computing the Mass and Center of Mass of a Lamina 4 Computing the Moments of Inertia of a Lamina Section 13.3 Double Integrals in Polar Coordinates...
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This note was uploaded on 03/05/2014 for the course MATH 101c taught by Professor Loukianoff,v during the Spring '08 term at Ohlone.

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