Recent content by ktvphysics

Yes. I figured it out. thank you, though

Homework Statement find the volume using spherical coordinates of the region bounded above by z=9 and below by z=sqrt(x^2+y^2) in the first octant. Homework EquationsThe Attempt at a Solution I found this volume using cartesian and cylindrical coordinates, so I know the answer I am looking...

I got 12pi for my final answer. ∫∫∫ r dzdrdΘ. 1/2r^2≤z≤6-r^2, 0≤r≤2, 0≤Θ≤2π = 12 pi

Integrate the radius from 0 to 2.

I'm not sure what you mean by that last bit... The part about the slice through the z-x plane The maximum value of the radius is 2, right? x^2 + y^2 = 4. sqrt(4) = 2. That was my mistake, I forgot to take the square root of 4. So I would integrate dr from 0 to 2, correct?

Ah, okay. I would have ran into that issue when I tried to solve it I guess. So x^2 + y^2 = r^2, yes? Can you explain why I integrate dr from 0 to 4? Why not 0 to 3? what does the intersection of the surfaces have to do with it?

Circles. Got it. So is this how I set it up? ∫∫∫ rdzdrdΘ , integrating dz from z= 1/2(x^2+y^2) to z = 6 - x^2 - y^2, dr from 0 to 4 and dΘ from 0 to 2π

I think I know how to solve it using a triple integral now. Solve it as a volume of rotation and we can compare answers, if you would like.

I know that the intersection of the two surfaces forms a plane that is a circle of radius 4. (I set the z equations equal to each other and found x^2 + y^2 = 4). Is every cross sectional area a circle, or is that only in this instance? After thinking about it, I am retracting my statement in the...

Yes, I must solve with a triple integral.

Yes, I agree. What you said is basically my progress so far.

Homework Statement I need to find the volume of an egg with a shape described by: z = 1/2(x2 + y2) and z = 6 - x2 - y2 I am also given that the egg is 6cm in length.Homework Equations I roughly graphed the two surfaces. The first being paraboloid that opens up from the origin, and the second...

So the answer to 2 would be: Isystem = 1/2 M(R23 + R24) + 2[1/2m(R21 + R22) + md2] That corrects the problem about the Parallel Axis Theorem, but I'm confused about what you were saying about the holes in the middle. I used the moments of inertia for hollow cylinders for the CD and Washers...

Answer check please -- Moment of Inertia Calculations For question 1 I got T=mnut * r pulley * gravity For question 2 I got Isystem = 1/2 M(R23 + R24 + m (R21 + R22) First day of physics lab and I just wanted to double check that these are correct. Thanks.