Question

which of these configurations in a gear train would cause increased speed?
two gears of the same size
a small gear driving a big gear
a big gear driving a small gear

Explanation:

In a gear train, the speed relationship between gears is based on the principle of gear ratios. The gear ratio \(r=\frac{N_2}{N_1}=\frac{\omega_1}{\omega_2}\), where \(N\) is the number of teeth and \(\omega\) is the angular velocity. When a big gear (driving gear, \(N_1\)) drives a small gear (driven gear, \(N_2\), \(N_2 1\), \(\omega_2>\omega_1\), which means the speed of the driven gear is increased.
When two gears of the same size (\(N_1 = N_2\)), \(\omega_1=\omega_2\), there is no speed change. When a small gear drives a big gear (\(N_2 > N_1\)), \(\omega_2=\frac{N_1}{N_2}\omega_1\), \(\frac{N_1}{N_2}<1\), \(\omega_2<\omega_1\), the speed of the driven gear is decreased.

Answer:

A big gear driving a small gear