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 ti
2 answers:
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By vector addition.
In fact, velocity is a vector, with a magnitude intensity, a direction and a verse, so we can't simply do an algebraic sum of the two (or more velocities).
First we need to decompose each velocity on both x- and y-axis (if we are on a 2D-plane), then we should do the algebraic sum of all the components on the x- axis and of all the components on the y-axis, to find the resultants on x- and y-axis. And finally, the magnitude of the resultant will be given by
where Rx and Rx are the resultants on x- and y-axis. The direction of the resultant will be given by
where
is its direction with respect to the x-axis.
In fact, velocity is a vector, with a magnitude intensity, a direction and a verse, so we can't simply do an algebraic sum of the two (or more velocities).
First we need to decompose each velocity on both x- and y-axis (if we are on a 2D-plane), then we should do the algebraic sum of all the components on the x- axis and of all the components on the y-axis, to find the resultants on x- and y-axis. And finally, the magnitude of the resultant will be given by
where Rx and Rx are the resultants on x- and y-axis. The direction of the resultant will be given by
where