Physics Problem: Helicopter Rotor Blades Moment of Inertia and Torque Calculation

What is the moment of inertia of three helicopter rotor blades about the axis of rotation and how much torque is needed to bring the blades up to a speed of 5.0 rev/s in 8.0 s? To determine the moment of inertia for three helicopter rotor blades, one multiplies the moment of inertia of a single blade by three. Then, using the angular acceleration derived from the desired rotational speed and time interval, the required torque to achieve that speed in the given time can be calculated.

Moment of Inertia Calculation

Moment of Inertia Formula: I = 1/3 * m * l^2 (where I is the moment of inertia, m is mass, and l is length)

Given that each rotor blade has a mass of 160 kg and a length of 3.75 m:

For one blade: I = 1/3 * 160 kg * (3.75 m)^2 = 700 kg·m^2

For three blades: Itotal = 3 * 700 kg·m^2 = 2100 kg·m^2

Torque Calculation

First, determine the angular acceleration (α) using the formula ω = α * t:

Given ω = 5.0 rev/s * 2π = 10π rad/s and time interval t = 8.0 s:

Angular acceleration α = (10π rad/s) / 8.0 s = π/4 rad/s^2

The torque required to bring the blades up to speed is τ = I * α:

Torque τ = 2100 kg·m^2 * π/4 rad/s^2 = 525π kg·m^2/s^2

Therefore, the motor needs to apply a torque of 525π kg·m^2/s^2 to achieve the desired speed in 8.0 seconds.

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