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Answer :
The rotation rate of the propeller at impact is equal to the initial rotation rate, which is 23.0 rev/s. the propeller's rotation rate at impact, taking into account air resistance, is approximately 20.5 rev/s.
To find the rotation rate of the propeller at impact, we can use the principle of conservation of angular momentum. The initial angular momentum of the propeller can be calculated using the formula: L_initial = I × ω_initial. where L_initial is the initial angular momentum, I is the moment of inertia, and ω_initial is the initial rotation rate. The final angular momentum of the propeller at impact can be calculated using the formula: L_final = I × ω_final, where L_final is the final angular momentum and ω_final is the final rotation rate.
Since angular momentum is conserved, we have: L_initial = L_final. Substituting the values given: I × ω_initial = I × ω_final. Canceling out the moment of inertia (I) from both sides ω_initial = ω_final. Therefore, the rotation rate of the propeller at impact is equal to the initial rotation rate, which is 23.0 rev/s. If air resistance is present and reduces the propeller's rotational kinetic energy by 33.0% at impact, the final rotation rate can be calculated using the formula: ω_final = √(1 - 0.33) × ω_initial
Substituting the value of ω_initial = 23.0 rev/s, we get: ω_final = √(1 - 0.33) × 23.0 rev/s. Calculating the value: ω_final ≈ 0.887 ×23.0 rev/s. Therefore, the propeller's rotation rate at impact, taking into account air resistance, is approximately 20.5 rev/s.
To learn more about kinetic energy, click here: brainly.com/question/22174271
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