Define Centre Of Mass Of A Rigid Body. Will It Be Always At The Geometrical Centre Of The Body? (2023)

FAQs

Define Centre Of Mass Of A Rigid Body. Will It Be Always At The Geometrical Centre Of The Body? ›

In the case of a rigid body, the centre of mass is fixed in relation to the body, and if the body has a uniform density, it will be located at the centroid.

Whenever an object does not have geometrical symmetry, its center of mass does not lie inside the body. For shapes like rings, the center of mass lies outside too. This is one of the possibilities of the position of the center of mass and is not necessarily always true.

For example, centre of mass of a uniform rod lies at its geometrical centre which lies within the rod whereas centre of mass of a uniform ring lies at its geometrical centre which lies outside the ring.

Centroid vs Center of Mass

From the previous definitions can be seen that the centroid is just influenced by the geometry of the system while the center of mass is influenced by both the geometry and the mass distribution in that geometry. The center of mass could be seen as a “mass powered centroid”.

No it's not necessary that the centre of mass of a body should lie inside the body. Consider a circular ring, its centre of mass lies at the center of the ring where there is no content of the body. So it can also lie outside the body .

The two do not always coincide, however. For example, the Moon's centre of mass is very close to its geometric centre (it is not exact because the Moon is not a perfect uniform sphere), but its centre of gravity is slightly displaced toward Earth because of the stronger gravitational force on the Moon's near side.

The centroid is the center of mass, while the mean center is the average of its vertices.

Generally the centre of mass lies inside the body but the position may change. Centre of mass depends on the shape and its mass distribution for a continuous distributed object. The center of mass need not lie within the body. This happens when the body does not have a geometrical symmetricity.

So, a solid rigid symmetrical body has a center of mass lying inside the body. The object is hollow or its mass distributed entirely on its circumference as in a case of ring or concentric circle. For these, the center of mass will be at kits center, where there is no mass present.

In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure.

Does center of mass depend on shape? ›

The position of centre of mass of a body depends on shape, size and distribution of mass of the body. The centre of mass does not lie necessarily at the centre of the body. Many objects have a point,a line or a plane of symmetry.

The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe.

If the object is uniform, the center of gravity of it will be at the exact geometric center. For example, the center of gravity of a circle is its center.

The correct option is B True

The centre of mass of a uniform circular ring or a disc lies at its geometric centre.

The center of mass of an object is always located inside the geometric bounds of the object. False. An unaided object will topple over when it's center of gravity extends beyond its support base.

Generally the centre of mass lies inside the body but the position may change. Centre of mass depends on the shape and its mass distribution for a continuous distributed object. The center of mass need not lie within the body. This happens when the body does not have a geometrical symmetricity.