Question

A 36-tooth gear turns three times. It is connected to a 12-tooth gear. How many times does the 12-tooth gear turn?

Answer 1

Hint: Two gears are meshed together with different numbers of teeth. The bigger has 36 teeth while the smaller has 12 teeth. The ratio of the number of teeth on both gears is called gear ratio. Since they are moving over one another, they move with the same speed. When smaller gear completes its round, the same number of teeth on the bigger gear also move through a fixed point.

Formula used:
$r=\dfrac{{{t}_{1}}}{{{t}_{2}}}$

Complete answer:
When two or more gears are connected together to transfer power between shafts, then such gears are known as meshed gears. The bigger of the two gears is known as gear while the smaller gear is called the pinion.

The gear ratio is the ratio of the number of teeth present in gear to the number of teeth present in the pinion. Let the number of teeth in gear be ${{t}_{1}}$ and the number of teeth in the pinion be ${{t}_{2}}$, then the gear ratio, $r$ will be-
$r=\dfrac{{{t}_{1}}}{{{t}_{2}}}$

When the pinion with 12 teeth turns it passes the point where they are meshed. Similarly the gear with 36 teeth also passes that point. Both gears are moving with the same speed. Therefore, we can say that when 12-teeth gear turns once, the 12 teeth of the 36-teeth gear also complete their turn.

Therefore, 1 turn of 12-teeth gear= $\dfrac{36}{12}=\dfrac{1}{3}$. 1 turn of 12-teeth gear is ${{\dfrac{1}{3}}^{rd}}$ of 36-teeth gear.

Therefore, 3 turns of pinion makes one turn of gear.

Since, the 36-teeth gear turns 3 times, 12-teeth gears turns $3\times 3=9\,times$.

Therefore, when 36-teeth gear turns 3 times, the 12-teeth gear turns 9 times.

Note:
A gear has three main functions, they are; increasing torque of driven equipment more than the driving equipment, to decrease the speed generated by the motor and to change the direction of the shafts. The gear ratio also depicts the ratio of output torque to the inner torque.