Calculus 3: Triple Integrals (24 of 25) Finding the Centroid: Center of Mass

In this video I will find the centroid (center of mass) of a semi-sphere.

Next video in this series can be seen at:

[HamedNourifar-ityf]

Thanks Sensei, but you should repalce the last theta with phi

[snnswn]

In this example, we assumed that density is constant. That's why it didn't show up in the formula. Right?

[sulphurnewsnetwork]

Pls help..A solid in the shape of a hemisphere with a radius of 2 units, has its base in the xy-plane
and the centre of the base at the origin. If the density of the solid is given by the function
ρ(x, y, z) = xyz, determine the mass of the hemisphere.

[ikennao]

how did you just Plug R into P ? where did the P didapper to ? 3:13

[lordyabo]

Sir, does this formula is always applicable to any situation?

[mightylini]

could you explain again how you went from integral sin(theta) * cos(theta) to 1/2*-cos(2*theta)? Isn’t integral sin(theta) * cos(theta) = -1/2*cos^2(theta)?

[laninez]

I got 3R/4 as the COM. Is that correct?

[wcruzwc]

Should have been (1/2 sin phi . dphi), not (1/2 sin theta . dphi)