Problem M. 406. (September 2021)

M. 406. At home make an inclined plane of small and variable angle of inclination. Fix the slope at a certain angle of inclination of \(\displaystyle \alpha\). Place a cylinder-shaped pencil on the slope such that the symmetry axis of the pencil makes an angle of \(\displaystyle \beta\) with a horizontal line lying in the plane of the slope. Investigate, at a certain fixed angle of \(\displaystyle \alpha\), at which angle of \(\displaystyle \beta\) will the pencil begin to move along the plane such that it

\(\displaystyle a)\) slides down, but does not roll at all;

\(\displaystyle b)\) rolls down without slipping?

Investigate the rolling and slipping regions, and plot them in a coordinate system of \(\displaystyle (\alpha,\beta)\).

(6 pont)

Deadline expired on October 15, 2021.

Statistics:

12 students sent a solution.
6 points:	Jeszenői Sára.
5 points:	Kovács Barnabás, Novák Péter.
4 points:	1 student.
3 points:	1 student.
0 point:	1 student.

Problems in Physics of KöMaL, September 2021