__Centre of Mass__

The centre of mass of a mass distribution in space (also known as the balancing point) is the unique location in physics where the weighted relative position of the dispersed mass adds to zero. A force can be applied to this location to create a linear acceleration without causing an angular acceleration. When stated with regard to the centre of mass, mechanics calculations are frequently simplified. It is a hypothetical point at which an object’s whole mass might be imagined to be concentrated in order to visualise its motion. To put it another way, the centre of mass is the particle equivalent of a particular object when Newton’s equations of motion are applied.

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In the case of a single rigid body, the centre of mass is fixed in respect to the body, and it will be placed at the centroid if the body has uniform density. The centre of mass of hollow or open-shaped objects, such as a horseshoe, can occasionally be found outside the physical body. The centre of mass may not match to the position of any particular member of the system in the event of a distribution of distinct bodies, such as the planets of the Solar System. The equations of motion of planets are expressed as point masses centred at the centres of mass in orbital mechanics. The centre of mass frame is an inertial frame in which a system’s centre of mass is at rest with relation to the coordinate system’s origin.

Definition: The centre of mass is a single point in space in the centre of a mass distribution that has the property that the weighted position vectors related to it total to zero. In the same way that the centre of mass is the mean position of a distribution of mass in space, the centre of mass is the mean location of a distribution of mass in space.

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__Centre Of Gravity__

The centre of gravity of a body is the point at which the torque caused by gravity forces disappears. When a gravitational field is uniform, the mass-centre and the centre-of-gravity will be the same. In the absence of other torques given to a satellite in orbit around a planet, the minor change (gradient) in gravitational field between closer-to (stronger) and further-from (weaker) the planet might result in a torque that will tend to align the satellite such that its long axis is vertical. It’s critical to distinguish between the centre-of-gravity and the mass-centre in this situation. Every horizontal difference between the two will lead to torque being applied. It’s worth noting that the mass-centre of a rigid body (e.g., with no slosh or articulation) is a fixed attribute, whereas the centre-of-gravity can change depending on its orientation in a non-uniform gravitational field. In the latter scenario, the centre-of-gravity will always be closer to the primary attractive body than the mass-centre, changing its location in the body of interest as its orientation changes.

Forces and moments must be resolved relative to the mass centre when studying the dynamics of aeroplanes, vehicles, and boats. That is true regardless of whether gravity is taken into account. The term “centre-of-gravity” is a slang term for the mass-centre, although it is widely used, and when gravity gradient effects are minor, the terms “centre-of-gravity” and “mass-centre” are interchangeable. Consider the resultant of gravitational forces on a continuous body in physics to show the benefits of utilising the centre of mass to describe a mass dispersion. Assume a body Q with a volume V and a density (r) at each location r. The force f at each point r in a parallel gravity field is given by:

__Locating The Centre of Mass__

The centre of mass of a body may be determined experimentally using gravity forces on the body and is based on the fact that the centre of mass is the same as the centre of gravity in the parallel gravity field at the earth’s surface. A body with a symmetry axis and constant density must have its centre of mass on this axis. As a result, the centre of mass of a circular cylinder with constant density is located on the cylinder’s axis. The centre of mass of a spherically symmetric body with constant density is also in the sphere’s centre. In general, the centre of mass of a body will be a fixed point of that symmetry for any symmetry. Suspending the item from two points and dropping plumb lines from the suspension points is an experimental approach for finding the centre of mass. The centre of mass is found at the junction of the two lines.

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