Question

The engine of a small airplane has a torque of 55.0Nm. The engine drives a propeller that is 2.1 m long (this is the length of one blade, not the diameter of the propeller), with mass m=41.0 kg. How long does it take the propeller (which you can model as a long rod) to reach 200rpm ?

Answer 1

To find the time it takes for a propeller to reach 200 rpm, calculate the moment of inertia, use Newton's second law for rotation to find angular acceleration, then use kinematic equations for angular motion to solve for time.

Step-by-step explanation:

To calculate the time it takes for a propeller to reach 200 rpm from rest given a torque of 55.0 Nm, we first need to find the moment of inertia of the propeller modeled as a long rod rotating about one end. The formula for the moment of inertia I of a rod of mass m and length L rotating about an end is I = (1/3) * m * L2. We can then use the relationship between torque (τ), moment of inertia (I), and angular acceleration (α) given by Newton's second law for rotation: τ = I * α. The angular acceleration can be found by re-arranging this formula to α = τ / I.

Next, we convert the final angular speed from rpm to rad/s and use the kinematic equation for angular motion ωf = ω0 + α * t, where ω0 is the initial angular speed (0 rad/s), ωf is the final angular speed, α is the angular acceleration, and t is the time. This equation can be solved for t to find the time it takes for the propeller to reach the final angular speed.