Center of Mass, Moment of Inertia, & Rotational Equilibrium

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