Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2023 / Paper 2 / 19 / b / i

Table of contents
- Solution i

Solution

The volume form in cylindrical coordinates is

d V = r d r d ϕ d z

. Integrating around the axis and over the height gives cylindrical-shell volume

2 πh r d r

. Hence the volume integral is

K = πh \int_{0}^{a} r v (r)^{2} d r = πh \int_{0}^{a} r^{3} ω (r)^{2} d r .

For unit density, this is the kinetic energy of the rotational motion.

 Ancestors (13)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version