The arc length L of a curve given parametrically by
(x(t), y(t)) for a ≤ t ≤ b
is given...
Mathematics, 25.11.2020 08:00 raizagisselle1694
The arc length L of a curve given parametrically by
(x(t), y(t)) for a ≤ t ≤ b
is given by the formula
L = integral a to b(x '(t))2 + (y '(t))2dt
A path of a point on the edge of a rolling circle of radius R is a cycloid, given by
x(t) = R (t − sin t),
y(t) = R (1 − cos t),
where t is the angle (in radians) the circle has rotated.
Find the length L of one "arch" of this cycloid, that is, find the distance traveled by a small stone stuck in the tread of a tire of radius R during one revolution of the rolling tire.
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