# Rotating Gears

Two gears $$A$$ and $$B$$ are meshing together as shown above. The numbers of cogs on each gear are $$12$$ and $$24$$, respectively, and $$3$$ red dots $$x,$$ $$y$$ and $$z$$ are marked on the two gears. Both gears are in uniform circular motion, and the radii of the rotating circles $$x$$, $$y$$ and $$z$$ are $$r$$, $$2r$$ and $$r$$, respectively. Which of the following statements is correct?

a) The period of point $$x$$ is the same as that of point $$z$$.
b) The angular speed of point $$x$$ is greater than that of point $$y$$.
c) The magnitude of acceleration of point $$y$$ is greater than that of point $$z$$.

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