Question

A gear system has one wheel with 10 teeth and the other wheel with 50 teeth. Calculate the gain in speed and the gain in torque that you can obtain using them. What will be the gear ration in each case?

Answer 1

Number of teeth in first wheel = 10
Number of teeth in second wheel = 50
For gain in speed, the second wheel of 50 teeth (NA = 50) is used as driving wheel and the first wheel of 10 teeth (NB = 10) is used as driven wheel.

Gear ratio =   `N_A /N_B` = `10/50`  = `1/5` = 1:5

Gain in speed = `N_A /N_B` = `50/10` =  `5/1` = 5

For gain in torque, the second wheel of 50 teeth (NB = 50) is used as driven wheel and the first wheel of 10 teeth (NA = 10) is used as driving wheel.

Gear ratio =    `N_A /N_B` =  `50/10` = `5/1`=5:1

Gain in torque =  `N_A/N_B`  = `10/50`= `1/5` = 1:5

Gain in torque  =  `N_B/N_A` `50/10` = 5