Rotating Gears

Classical Mechanics Level 3

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 $z$ .

b) and c) c) only b) only a) and b)

1 solution

Ronald Das
Apr 29, 2014

The angular speed of gear A is two times that of B ( same no of cogs must be meshing up.. Therefore the ratio is 12:24=1:2). So the time period of x and z can't be same. And the centripetal acceleration is directly proportional to distance from the center ( If the angular speeds are same). So z has higher acceleration than y.

Rotating Gears

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