# Relationship between center of gravity and moment inertia

### How to measure moment of inertia through the center of gravity without knowing the CG location

Center of Gravity and Moment of Inertia are the two most important basic concept for Structural miyagi-marugoto2012.info possible to do any analysis or. even without knowing the center of gravity location 1. Why measure Moment of Inertia (MOI) through the Center of Gravity (CG)? When an object is free to rotate, . The center of gravity is a place. The moment of inertia is a property of a rigid body .

In other words, if your moment of inertia measurement instrument has 0. From one measurement to the next, the payload must be translated in a horizontal plane, without changing its orientation. Moment of inertia measurements give best results when the center of gravity of the payload is located close to the machine centerline.

Therefore, measurement positions must be chosen carefully to stay within the tolerance of the instrument for overturning moment, but to provide as great a variation as possible from one position to the next. Fixturing is crucial for these measurements. The use of a two axis translation table allows measurements without refixturing the payload. Can I find center of gravity location with this method? What accuracy can I expect?

## Center of Gravity and Moment of Inertia

This method will give you a rough estimate of center of gravity location, but the uncertainty is very large. Do not rely on this method to give you a center of gravity location that you can use in calculation or for balancing purposes.

Accuracy depends on your payload. How does Space Electronics implement this method? We design custom software and fixtures that automate the measurement and calculation process.

The torque produced by a force F is also defined as Fd. The two terms are synonymous. Forces F1 and F2 produce a counterclockwise torque and forces F3, F4 and F5 produce a clockwise torque. The law of the lever states that in order to have equilibrium the sum of the counterclockwise torques or moments must be equal to the sum of the clockwise torques. If the sums are not equal there will be rotation.

Computing centers of gravity. We wish now to deal with the problem of computing the location of the center of gravity, or center of mass, of a body.

### Center of Gravity and Newton's Second Law in Rotation

The center of gravity is the same as the center of mass since weight and mass are proportional. However, in developing the ideas involved we need to assume a gravitational field and will speak of the center of gravity. In developing the ideas for computing the location of the center of gravity we will view a body as an assemblage of individual particles.

The earth exerts an attraction on each individual particle of a body and the weight of a body is the sum total of all the forces on all the particles making up the body.

Thus we will consider the problem of finding the location of the center of gravity for assemblages of particles in space.

Consider a steel rod resting on a pivot as shown in Fig. If the pivot is directly below the center of gravity, the rod is balanced, and the sum of all the clockwise moments from particles to the right of the pivot is equal to the sum of all the counterclockwise moments from the particles to the left of the pivot.

The upward force F exerted by the pivot on the rod, as shown in Fig. Now let us consider the situation in which the pivot is at the left end of the rod as shown in Fig. Suppose an upward force F is exerted directly below the center of gravity and equal in magnitude to the weight of the rod. Then the rod will be balanced, no force will be exerted on the pivot, and the sum of all of the clockwise moments from the particles of the rod will be equal to the counterclockwise moment Fd produced by force F where d is the distance from the pivot to the center of gravity, as shown in the figure.

Thus if we were able to compute the clockwise moments of the particles of the rod with respect to the pivot point and knew the weight of the rod, we would then be able to compute the distance d from the pivot to the center of gravity.

Consider now a system of n point masses situated along a horizontal line, as shown in Fig.