Question

if my engine has 10 teeth, and my propeller has 30 teeth; my engine is spinning at 2800 rpm, what is my propeller spinning at? rpm

Explanation:

Step1: Recall Gear Ratio Concept

The relationship between engine RPM (\(N_e\)), engine teeth (\(T_e\)), propeller RPM (\(N_p\)), and propeller teeth (\(T_p\)) is based on the gear ratio: \(N_e \times T_e = N_p \times T_p\) (since the number of teeth - rpm product is constant for meshed gears/gearing systems).

Step2: Identify Given Values

We know \(N_e = 2800\) RPM, \(T_e = 10\) teeth, \(T_p = 30\) teeth. We need to find \(N_p\).

Step3: Rearrange Formula for \(N_p\)

From \(N_e \times T_e = N_p \times T_p\), we can solve for \(N_p\): \(N_p=\frac{N_e \times T_e}{T_p}\)

Step4: Substitute Values

Substitute \(N_e = 2800\), \(T_e = 10\), \(T_p = 30\) into the formula: \(N_p=\frac{2800\times10}{30}\)

Step5: Calculate the Result

First, calculate the numerator: \(2800\times10 = 28000\). Then divide by the denominator: \(\frac{28000}{30}=\frac{2800}{3}\approx933.33\) RPM (or as a fraction \(\frac{2800}{3}\) RPM).

Answer:

The propeller is spinning at \(\frac{2800}{3}\approx933.33\) RPM.