The discussion revolves around calculating the gravitational acceleration at an arbitrary location due to a disc characterized by its thickness, radius, and density. The problem involves understanding how gravity behaves in relation to the disc's geometry and mass distribution.
The discussion is active, with participants exploring different interpretations of the gravitational field around the disc. Some guidance has been offered regarding the treatment of the disc as a point source for cases outside the disc, but there is no consensus on the implications of this for points along the axis versus at the edge of the disc.
Participants assume that the density and thickness of the disc are constant. There is an acknowledgment of the complexity introduced by the geometry of the disc, particularly in distinguishing between cases inside and outside the disc.
Welcome to Physics Forums.bumpkin said:Homework Statement
calculate the gravity acceleration at an arbitrary location due to a disc of thickness h, radius r and density p
Homework Equations
g=Gm/r^2
The Attempt at a Solution
define r in terms of the vector magnitude from the measurement point to some point on the disc, then hit it with a volume integral? Is there an easier way, say using symmetry?
Hootenanny said:Welcome to Physics Forums.
I'm assuming that rho and h are constant.
It may well be easier to tackle this problem in two separate cases: (a) When the point of interest is outside the body; and (b) when the point of interest is inside the body. For the former case, the gravitational field of the disc is identical to that of a point source of equivalent mass, located at the centre of the disc.
That would be true for a uniform sphere, but not for a disk.Hootenanny said:For the former case, the gravitational field of the disc is identical to that of a point source of equivalent mass, located at the centre of the disc.
Oh, sorry. I assumed that you were working in 2D, in the plane of the disc. My bad.bumpkin said:rho and h are constant. I hadn't even thought of b. But for a, I would assume the acceleration at the edge of the disc would be different to the gravity long the axis of the disc? Ie if the disc was in the xy plane, the gravity at (r,0,h) would be different to (0,0,sqrt(r^2+h^2))?