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How to Create a Beam Moment Equation

The moment of inertia is a measurement of how easy or difficult an object is to rotate. It is a function of how heavy an object is and how far away its center of mass is from its axis of rotation. For instance, it is harder to swing a sledge hammer when you hold onto the handle than when you hold onto the head. The greater the weight, the further away it is from its pivot, the greater the moment of inertia is. Whether you are studying rotational motion in class or are working with steel beams in a construction project, you need to know how to determine the moment of a beam.

Things You'll Need

Measuring tape
Scale
Calculator

Instructions

- 1
  Measure the distance from the pivot, or axis the beam will rotate around, to one end of the beam. Label this distance "D." Measure the distance from the pivot to the other end of the beam. Multiply this distance by negative one. Label this figure "L." If the beam is rotating about one of its ends, then L is equal to zero.
- 2
  Weigh the beam. If the beam weighs too much to make using the scale impractical, then measure the volume of the beam and multiply it by the density of the material it is made out of. If the beam is rectangular, its volume is its length multiplied by its width multiplied by its height. If it is an I-beam, the volume is equal to the volumes of its three rectangular sections added together. If the beam is cylindrical, it is equal to its radius squared multiplied by pi, then multiplied by its length.
- 3
  Cube D, or multiply it by itself twice. Multiply the result by the weight of the beam. Divide this result by the length of the beam. Divide it by three. Label this value "M." Cube L, multiply the result by the weight of the beam, divide it by the length, then divide it by three. Label this result "N." Subtract N from M. The result is the moment of inertia of the beam.
- 4
  Write the moment of inertia of the beam, followed by the equals sign. On the other side of the sign, write the expression for M followed by a minus sign and then followed by the expression for N. This is the equation for the beam moment.

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