OHHHHH! Hot damn, no wonder the answer looks similar like yours but just doesn't quite add up lol, didn't realize i was doing a mixture of it. Now i see what i am doing wrong, been scratching my head day and night haha.
Thank you very much for your assistance vela! I can't thank you enough...
I ran into problems trying to find the mass, i was under the impression that the only way to get the mass was to subtract the values, but i didn't know what limits to use haha, and thank you very much vela! I now too realize there is no use for subtraction.
I'll just write out a long equation...
Okay, my answer is wayy different than yours, i can see a square root of 3 and from that i know i must should be using r = 2 cos θ and θ = π/3 for my calculation
Okay so i am confused as to which limits of θ i should be using, it will either be π/3 or π/2, but based on the diagram above i should be using -π/3 and π/3 because that angle is bounded where r=0 and r=1.
After subtracting the masses the final mass is 4Kπ/9 + 8K/3
Is this correct? Because...
Thank you very much vela, okay so i used the coordinates at the intersection points to try and get the angle, and based on what you said above when the angle is between 0 and 60 degrees, r is bounded by 0 and circle 2.
So does that mean if the angle is more than 60 degree, r will be bounded by...
for the mass i i took the total mass of circle 1 (ie: 0 ≤ r ≤ 2 cos θ, -π/2 ≤ θ ≤ π/2) minus the part where the two circles overlap (ie: 1 ≤ r ≤ 2 cos θ, -π/2 ≤ θ ≤ π/2) and i got
mass= Kπ/3
than i used these limits 1 ≤ r ≤ 2 cos θ, -π/2 ≤ θ ≤ π/2 to calculate the moment and i got
moment=...
Ahha! Its much clearer to me now, thank you very much vela. However I'm still wondering which I couldn't integrate and subtract the two circles to get the mass...
Thank you very much for your help vela, much appreciated. So if i got this correctly, my mass should be:
m =∬ρ(r,θ)rdrdθ, where the domain is 1 ≤ r ≤ 2 cos θ and π/6 ≤ θ ≤ 5π/6 and p(r,θ) = Kr?
And when i get the mass, i follow the steps below to get the centre of mass:
1/m ∫∫ x(Kr) r...
Oh let me clarify for the mass, I used polar coordinates: ∫∫ (Kr) r dr dθ and the domains are, for circle 1: 0 ≤ r ≤ 2 cos θ and -π/2 ≤ θ ≤ π/2 and for circle 2: 0 ≤ r ≤ 1 and 0 ≤ θ ≤ 2π, I integrated them and subtracted them. I'm kinda lost as to which θ I should to...
Homework Statement
Find the centre of mass of the 2-dimensional plate which occupies the region inside the circle x^2+y^2=2x, but outside x^2+y^2=1, and for which the density is proportional to its distance from the origin.
Homework Equations
Centre of mass for x coordinate: 1/m ∫∫ x ρ(x,y)...
Homework Statement
f(x,y) = ln(3y-8x)
Derive the first and second order Taylor polynomial approx, L(x,t) and Q(x,t), for T(x,T) about the point (1,1)
Homework Equations
-None-
The Attempt at a Solution
I do not understand what the question wants, nor do i want a solution. I...