How many teeth does a driven gear have if a gear wheel with 85 teeth rotates at 6,500 r/min and drives it at 9,866 r/min?

To determine the number of teeth on the driven gear, we can use the relationship between the speeds of the gears and the number of teeth they have. The formula linking these variables is:

[

\frac{T_1}{T_2} = \frac{N_2}{N_1}

]

where:

• (T_1) is the number of teeth on the driver gear,

• (T_2) is the number of teeth on the driven gear,

• (N_1) is the speed of the driver gear (in r/min),

• (N_2) is the speed of the driven gear (in r/min).

In this case, we know:

• The driver gear has 85 teeth (T1 = 85),

• It rotates at 6,500 r/min (N1 = 6500),

• The driven gear rotates at 9,866 r/min (N2 = 9866).

Rearranging the formula to solve for (T_2):

[

T_2 = T_1 \times \frac{N_1}{N_2}

]

Substituting in the known values:

[

T_2 =