Acoustics and Vibration Animations Daniel A. Russell, Ph.D. Graduate Program in Acoustics The Pennsylvania State University All text and images on this page are ©2004-2011 by Daniel A. Russell and may not used in other web pages or reports without permission.

# Motion of the Center of Mass

The animations on this page were inspired by the series of multiflash photographs in Figures 7-1 and 7-7 of F. W. Sears, Mechanics, Heat, and Sound, (Addision-Wesley, 1950).

The center-of-mass (COM) is the single point on a structure which characterizes the motion of the object if the object shrinks to a point mass. If a net force is applied to the COM the resulting motion will be translation (the object will not rotate). If a net force is applied to some other location on the object, the object will both translate and rotate about its COM. The animations below illustrate this concept.

## Impact at the COM => 1-D Linear Motion

 The movie at left shows an object which is more massive at one end than the other, so that the COM is located towards the larger (more massive) end. When the object is struck at the COM the object translates (moves in a straight line) but does not rotate about the COM. In the middle movie the object is struck to the right of the COM. Now the objects translates and rotates counterclockwise about the COM. Notice that the COM moves in the same straight line as it did when the impact was at the COM. This illustrates that the COM is the single point which characterizes the translational motion of the object. Now the object is struck to the left of the COM so that it translates and rotates clockwise about the COM. Notice, once again, that the COM moves in the same straight line as it did when the impact was at the COM. This again illustrates that the COM is the single point which characterizes the translational motion of the object.

## Impact at the COM => 2-D Projectile Motion

 The movie at left shows an object which is more massive at one end than the other, so that the COM is located towards the larger (more massive) end. When the object is struck at the COM the object does not rotate, but follows the trajectory of a projectile, just like a ball shot off the edge of a table. When the object is struck at a point above the COM, the object rotates clockwise about its COM, while at the same time the COM follows the original projectile path. Now the object is struck at a point below the COM, and it rotates counterclockwise while the COM follows the same projectile path.
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