Win_odd Dhamnekar
Junior Member
- Joined
- Aug 14, 2018
- Messages
- 207
Find the center of mass of the region R with the given density function \(\displaystyle \delta(x,y)\)
1)R = {(x,y) : y ≥ 0, x ≥ 0 , 1 ≤ x2 + y2 ≤ 4 }, \(\displaystyle \delta(x,y) = \sqrt{x^2 + y^2}\)
How to answer this question?
My attempt to answer this question:
[math]M = \displaystyle\int_0^2 \displaystyle\int_0^x (x^2+ y^2)^{\frac32}dy dx = 10.0348925582[/math]
Is this computation of M correct? How to compute M in cylindrical coordinates?
How to compute center of mass in any coordinates?(spherical, cylindrical, cartesian)
1)R = {(x,y) : y ≥ 0, x ≥ 0 , 1 ≤ x2 + y2 ≤ 4 }, \(\displaystyle \delta(x,y) = \sqrt{x^2 + y^2}\)
How to answer this question?
My attempt to answer this question:
[math]M = \displaystyle\int_0^2 \displaystyle\int_0^x (x^2+ y^2)^{\frac32}dy dx = 10.0348925582[/math]
Is this computation of M correct? How to compute M in cylindrical coordinates?
How to compute center of mass in any coordinates?(spherical, cylindrical, cartesian)