Find I x , I y , I 0 of a mass of density f(x,y) = 1
Question:
Find Ix, Iy, I0 of a mass of density f(x,y) = 1 in the region R in the figures, which the engineer is likely to need, along with other profiles listed in engineering handbooks.
R as in Prob. 13.
Data from Prob. 13
Find the center of gravity (x̅, y̅) of a mass of density f(x, y) = 1 in the given region R.
Step by Step Answer:
x 1A xfxydA y 1A yfxydA where A is the area of the region R Using the data from Prob 13 we ...View the full answer
Related Video
The Centre of gravity is a theoretical point in the body where the body’s total weight is thought to be concentrated. It is important to know the centre of gravity because it predicts the behaviour of a moving body when acted on by gravity. It is also useful in designing static structures such as buildings and bridges.In a uniform gravitational field, the centre of gravity is identical to the centre of mass. Yet, the two points do not always coincide. For the Moon, the centre of mass is very close to its geometric centre. However, its centre of gravity is slightly towards the Earth due to the stronger gravitational force on the Moon’s near side.
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