Classical Dynamics of Particles and Systems · Problem 5-20

Calculus of Variations — Marion & Thornton

Physics — Mechanics · gravitational-potential-disk

Problem

A thin disk of mass

M

and radius

R

lies in the

(x, y)

plane with the

z

-axis passing through the center of the disk. Calculate the gravitational potential

\Phi(z)

and the gravitational field

\mathbf{g}(z) = -\nabla\Phi(z) = -\hat{\mathbf{k}}\, d\Phi(z)/dz

on the

z

-axis.