Is uniform mass and continuous mass is same as uniform body and continuous body? Examples of uniform, non-uniform, continuous and non-continuous mass/bodies? Please also explain a little bit. while finding centre of mass of certain objects like rod, ball, square, or any irregular shape, these words are used.
closed as unclear what you're asking by Mike, Kyle Kanos, Jon Custer, Cosmas Zachos, M. Enns Mar 20 '18 at 23:42
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A discrete mass distribution is made up of point masses arranged in fixed relative positions. To find the mass, centre of mass or moment of inertia you use summation. The density of such a body is non-uniform, it varies from place to place : it is infinite at the point masses and zero elsewhere.
Discrete mass distributions are hypothetical. They don't exist in the real world because point masses don't exist. All mass occupies a finite amount of volume. However, if the mass of an object is concentrated in regions which are small compared with the size of the object, then those regions could be treated as point masses.
Examples : a dumbbell/barbell is usually treated as two point masses at the ends of a massless rod; a simple pendulum is a point mass at one end of a massless string or rod.
A continuous mass distribution is spread out in space. Every point within the body is connected to the whole, there are no gaps. If the density is the same at all points within its boundaries it is uniform. To find the mass, centre of mass or moment of inertia of a continuous body you might have to use an integral, ie a summation of an infinite number of infinitesimally small parts in which the density is uniform. Integration is usually necessary if the density varies from one place in the body to another.
Examples : a solid sphere or cube, which usually have uniform density if made out of a single material such as wood or iron. The Earth and other planets have non-uniform density; they are more compressed towards the centre because of gravity.
An object can be a mixture of continuous and discrete mass distributions.