#### Question

A gear system has the driving wheel of radius 2 cm and driven wheel of radius 20 cm.

(a) Find the gear ratio.

(b) If the number of rotations made per minute by the driving wheel is 100, find the number of rotations per minute made by the driven wheel.

(c) If the driven wheel has 40 teeth, find the number of teeth in the driving wheel.

#### Solution

The radius of driving wheel r_{A} = 2cm

The radius of driven wheel r_{B} = 20cm

(a) the gear ratio `r_A/r_B` = `2/20` = 1:10

(b) The number of rotations made per minute by the driving wheel is `n_a`= 100

The number of rotations made per minute by the driven wheel 𝑛𝑏= `r_A/r_B`×𝑛𝑎 = `2/20`×100=10

(a) Number of teeth in driven wheel nb = 40.

Number of teeth in driven wheel na =`"ra"/"rb"`× nb

⇒`2 /20 xx40` = 4.