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Physics 111

Lecture 26. Chapter 8: Center of Gravity Moment of Inertia. Friday, October 30, 1998. Physics 111. x. Or, in shorthand notation. (0,1) m 1 kg. (1,0) m 1 kg. (-1,0) m 2 kg. We can easily extend this to 2-dimensional objects by finding a center of mass in the y-direction:.

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Physics 111

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  1. Lecture 26 Chapter 8: Center of Gravity Moment of Inertia Friday, October 30, 1998 Physics 111

  2. x Or, in shorthand notation

  3. (0,1) m 1 kg (1,0) m 1 kg (-1,0) m 2 kg We can easily extend this to 2-dimensional objects by finding a center of mass in the y-direction: What is the center of mass of this system:

  4. (0,1) m 1 kg (1,0) m 1 kg (-1,0) m 2 kg CM "Weighted Averages"

  5. Concept Quiz! Center of Mass

  6. All the equations and laws we examined in linear motion assumed point masses. For extended (real) objects, these equations really describe the motion of the center of mass of the objects. The instantaneous velocity of a piece of an extended object may not equal the velocity of the center of mass.

  7. v vCM t For example, let’s look at the way this pillow flies across the room! If I just asked you to plot the horizontal velocity of the red square as a function of time, what would such a plot look like? Oscillates around the center of mass velocity--sometimes faster, sometimes slower.

  8. Based on our definition of the center of mass, the velocity of the center of mass can be obtained if we know the velocities of all the little pieces of our system. Similarly for the acceleration of the center of mass...

  9. Concept Quiz! CM Velocity

  10. FDt FDt w vCM vCM Clearly, the motion of the dumbells will be quite different, even though the velocity of the center of mass is identical.

  11. m r Ft pinned to table Torque & Angular Acceleration The tangential force results in a tangential acceleration.

  12. m r Ft pinned to table Torque & Angular Acceleration It also creates a torque about the pinned point.

  13. m r Ft pinned to table Torque & Angular Acceleration Recalling that tangential acceleration is related to angular acceleration, we get

  14. m r Ft pinned to table Torque & Angular Acceleration This expression is good so long as our connecting rod/string is massless.

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