A circle of circumference 1 m rolls around the equilateral triangle ABC of perimeter 3 m. How many turns does the circle make as it rolls around the triangle once without slipping?

Question

pythagoras123 · Answer

attachment

pythagoras123 · Answer

By the way, it would be good to show the reasoning/solution as to how you arrive at the answer. Thanks. :) 
P.S. The answer isn't 3 turns.

jlastino · Answer

4? I think when the circle goes around the corner there would be 1/3 of a rotation....so there are 3 corners and there would be an extra rotation?...idk lol

jlastino · Answer

the question is hard T_T

pythagoras123 · Answer

@Jlastino, why will there be 1/3 of a rotation for each corner?

anonymous · Answer

The circle shouldn't rotate around the corners. Presumably the same surface particle is in contact for the entire corner-movement, IF there is actually no slipping.

jlastino · Answer

because the radius is perpendicular to the side of the triangle we have to rotate the circle around the corner until that radius is perpendicular to the next side...the interior angles of an equilateral triangle = 60 degrees and we have  two perpendiculars, so the angle of rotation is 360 - (90+60+90) = 120....which is 1/3 of 360...?

anonymous · Answer

at the corners, the center of rotation is not the center of the circle but at the corner.  so the circle still has to rotate some amount to change direction.  that amount is actually the exterior angle of the triangle, 2/3 of a 180 degrees.....