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?
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the question is hard T_T
@Jlastino, why will there be 1/3 of a rotation for each corner?
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.
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...?
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.....