so, I'm confused at 1:44. when i use dimensional analysis to check the units for mass_slice, I get density * area = (kg/m^3) * (m^2) = kg/m. but clearly, kg/m are not the proper units for mass (or am i wrong? i'm not a physics student, never have taken a physics class). so i'm confused here since it would appear we aren't actually finding mass. edit: nevermind, i used the wrong definition of density. since we are working in a 2d environment, density in this case is area density (or kg/m^2). the units work out now
Can you explain mathematically why we can always find a line through a lamina (eg a horizontal line y=a in some coordinate system on the lamina) such that the moments on either side of this line sum to zero. It's intuitively obvious physically (hanging plumb lines etc) but I just can't prove this mathematically. The mathematics involves the integral of all the moments of every point mass of the lamina on either side of such a line, putting this integral equal to zero and solving for the coordinate of the centre of mass. But why can we always assume we can put such an integral equal to zero in the first place.
The explanation was very easy to understand. you made life so much easier. Thank you David! keep up the work.
thanks, I dont know Why is it so hard for people to just explain this stuff instead of popping canned formulas out of their asses.
Well, it's because they only know its use, not understand how it works.
This is what I was looking for
Legend
so, I'm confused at 1:44. when i use dimensional analysis to check the units for mass_slice, I get density * area = (kg/m^3) * (m^2) = kg/m. but clearly, kg/m are not the proper units for mass (or am i wrong? i'm not a physics student, never have taken a physics class). so i'm confused here since it would appear we aren't actually finding mass.
edit: nevermind, i used the wrong definition of density. since we are working in a 2d environment, density in this case is area density (or kg/m^2). the units work out now
Adorable! Thanks for the explanation
Thanks for helping sir!!👍
With lamina problems, we assume rho is an area density, not a volume density.
Ah! This is exactly what I was having issues with trying to understand my textbook's explanation. Thank you so much Dlipp!
Can you explain mathematically why we can always find a line through a lamina (eg a horizontal line y=a in some coordinate system on the lamina) such that the moments on either side of this line sum to zero. It's intuitively obvious physically (hanging plumb lines etc) but I just can't prove this mathematically. The mathematics involves the integral of all the moments of every point mass of the lamina on either side of such a line, putting this integral equal to zero and solving for the coordinate of the centre of mass. But why can we always assume we can put such an integral equal to zero in the first place.
YOU ARE AWESOME
Thank you
I think you forgot the summation. It has to be a double integral right?
u r insnae beast ty g