You will need
• the formula for calculating the center of mass.
Instruction
1
Note that the position of the center of mass depends on how distributed the volume of his body weight. The center of mass may not even be in the body, an example of such object is a homogeneous ring whose centre of mass is its geometric centre. That is – in the void. When calculating the center of mass can be considered a mathematical point, which focuses the whole body weight.
2
The concept of center of mass and center of gravity very close, so in the calculations, in most cases, they can be considered synonyms. The only difference is that the concept of center of gravity requires gravity and center of mass is present in the absence of gravity. The body is falling freely without rotation, moves under the force of gravity, applied to all its points, while its center of mass coincides with the center of gravity. To determine the center of mass in the classical mechanics uses the following formula.
3
Here R. TS.m. – the radius-vector of center of mass, mi – mass of i-th point, ri is the radius-vector of the i-th point of the system. In practice, in many cases, it is easy to find the center of mass if the object has a strict geometric form. For example, a homogeneous rod it is located exactly in the middle. The parallelogram at the intersection of diagonals of a triangle is the intersection point of the medians, and of a regular polygon center of mass is at the center of rotational symmetry. 4
For more complex bodies the task of calculation becomes complicated in this case, you must break the object into homogeneous volumes. For each of them separately calculated centers of mass, then the values are substituted in the appropriate formula is the final value.
5
In practice, the need to determine the center of mass (center of gravity) is typically associated with design. For example, when designing a vessel it is important to ensure its stability. If the center of gravity will be very high, the ship may capsize. How to calculate the right setting for such complex object like a ship? To do this, there are centers of gravity of the individual elements and units, and then the values are added based on their location. When designing the center of gravity generally placed as low as possible, so the most heavy units have at the bottom.