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Center of Mass, Moment of Inertia, & Rotational Equilibrium

Center of Mass, Moment of Inertia, & Rotational Equilibrium. Rotation Physics Mr. McCallister. Center of Mass. Center of mass is “the point at which all the mass of the body can be considered to be concentrated when analyzing translational motion”

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Center of Mass, Moment of Inertia, & Rotational Equilibrium

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  1. Center of Mass, Moment of Inertia, & Rotational Equilibrium Rotation Physics Mr. McCallister

  2. Center of Mass • Center of mass is “the point at which all the mass of the body can be considered to be concentrated when analyzing translational motion” • For simple objects of uniform density, the center of mass will be located at geometric center of the object. • However, the center of mass may not necessarily be located within the volume of the object (i.e. doughnut, boomerang).

  3. Center of Mass • If gravity is the only force acting on a rotating object: • The object will rotate about its center of mass • The center of mass will follow a parabolic trajectory (projectile motion)

  4. Center of Mass Fig 8-7, p. 283: A rotating object in free fall will rotate about its center of mass, which follows a parabolic flight path.

  5. Moment of Inertia • Moment of inertia is “the tendency of a body rotating about a fixed axis to resist a change in rotational motion” • In other words, moment of inertia is a measure of an object’s resistance to being rotated (similar to inertia being a measure of an object’s resistance to being accelerated) • Symbol: I , Unit: kg m2

  6. Moment of Inertia • Moment of inertia depends on how far the mass of the object is distributed in relation to the axis of rotation • Table 8-1 on p. 285 gives a list of common moments of inertia • Note that a single object has numerous moments of inertia, since the same object can be rotated in various ways

  7. Table 8-1, p. 285

  8. Rotational Equilibrium • For an object to be in translational equilibrium, its net force must be zero. • For an object to be in rotational equilibrium, its net torque must be zero. • For an object to be in total equilibrium, its net force and net torque must be zero. • Easiest concept, but most difficult problems…

  9. 8B, p. 288 #2-4, Section Review • Sample Problem 8B • Completed on board • Work due NEXT Tuesday 2-16-10

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