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))?
The gravity at an arbitrary location near a disc is not constant like that of a point mass. It varies depending on the distance from the disc's center and its mass distribution. The gravity near the edge of the disc is weaker compared to that near the center of the disc.
The strength of gravity near a disc is affected by the mass of the disc, the distance from the disc's center, and the distribution of mass within the disc. The gravity is stronger when the disc has a higher mass and when the distance from the center is smaller. Additionally, if the mass distribution within the disc is not uniform, the gravity will vary even at the same distance from the center.
No, the gravity near a disc can never be zero. As long as the disc has mass, it will always exert some level of gravitational force on objects around it. However, the gravity near the edge of the disc may be very weak compared to that near the center.
To calculate the gravity at an arbitrary location near a disc, we can use the formula for the gravitational field strength, which is given by GM/r^2, where G is the gravitational constant, M is the mass of the disc, and r is the distance from the center of the disc. We also need to take into account the mass distribution within the disc, which can be done through integration.
Yes, the gravity near a disc affects the motion of objects differently compared to the gravity of a point mass. This is because the gravitational force near a disc is not constant, so the direction and magnitude of the force will vary depending on the position of the object relative to the disc. In contrast, the gravity of a point mass is constant and always acts towards the center of the mass.