Re: effect of positions of weights on a bar

Hi Graham,

The reason why the heavier weights are placed inside the lighter ones is to lower the first moment of inertia of the system. All objects have 3 important moments of inertia that contribute to the feeling of "heaviness" in different circumstances: zeroth, first, and second moment.

The zeroth moment is the mass (or less technically the weight). The mass is the inertia that must be overcome to move the object along a line through the center of mass. The center of mass refers to the geometric spot in which all the mass can be considered to reside to balance the object. The center of gravity is the same thing as the center of mass except that it refers to a weight (mass * acceleration) instead of just mass.

The first moment is the measure of the mass distribution times distance relative to some point usual ly the point of an applied force or the geometric center of the object. The first moment times acceleration is torque. Any time a force is applied on a line not through the center of mass of an object -- a torque results. Consider a sledge hammer as a good example of first moment. Most of the mass is in the hammering end and very little in the shaft of the handle. Swinging the hammer requires a large amount of torque (mass * acceleration * length). When the first moment measured from the geometric center does not cancel to zero, then the center of gravity (or balance) is not in the middle of the object. To balance a regular hammer, you got to hold it on the shaft very close to the pounding end. The best example of first moment is a see-saw, lever, or crowbar. A mass at a distance X from the center of the see-saw will balance twice the mass at a distance X/2 on the other side.

The second moment is the measure of the mass distribution times distance squared relative to some point, usually the center of mass or center of rotation. The second moment is a measure of resistance to change in spinning rate. An object with a high second moment of inertia has much of i ts mass away from the axis of rotation and will spin slower than an object with its mass closer to the axis of rotation for a given energy. The classic example of second moment is an ice skater spinning fast er with her arms pulled in then when her arms are extended. However, a higher second moment gives more spin stability than a lower second moment. Other examples are a high wire walker's balance pol e or most gyroscopes.

When lifting a dumbbell or a longer bar with weight plates on it all three moments come into play. When you lift a bar with weights on it (like benching, military press, or any other really), you move the center of mass upward against gravity. If the weight on each end of the bar is the same, then the center of gravity will be in the middle of the bar. By lifting the bar with your hands evenly surrounding the center of gravity no lateral torque is created by the positioning of your hands. However, if one arm is stronger than the other or the weight is not distributed evenly, then a torque results that tries to rotate the weight bar (end over end). Putting the heavier weight inside the lighter weights minimizes the first moment effects in the case of an unbalanced lift (remember weight * distance is first moment or torque). Once the weight bar starts to rotate recovery is more difficult (especially if the weight clips are not used) when heavier weights are on the outside because the first and second moments are larger. If the weight clips are not used, then the weights on the low end of the bar could slide off and then the first moment way out of balance -- BAM, disaster.

Sincerely,

Tom "Curl Meister" Cull