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

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.