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Helicopter Kinetic Energy Breakdown

Apr 5, 2025

Helicopter Kinetic Energy: Rotational and Translational

Introduction

  • Discusses the kinetic energy of a helicopter, focusing on the rotational and translational energy of its components.
  • Key measurements:
    • Length of each blade: 5 meters
    • Mass of each blade: 60 kg
    • Total helicopter mass: 200 kg
  • Goals:
    • Calculate rotational kinetic energy of the blades.
    • Calculate translational kinetic energy of the helicopter.
    • Determine which type of kinetic energy is greater.

Rotational Kinetic Energy of the Blades

Rotational Speed Conversion

  • Blades rotate at 350 revolutions per minute (RPM).
  • Conversion from RPM to radians per second:
    • Formula: Multiply by π/30.
    • Result: 36.65 rad/s.

Moment of Inertia Calculation

  • Blades assumed as rods rotating about one end.
  • Formula for a rod: (I = \frac{ML^2}{3}).
  • For 4 blades: Total moment of inertia = 4 times individual blade inertia.
  • Calculation:
    • Mass (M) = 60 kg
    • Length (L) = 5 m
    • Result: Total inertia (I = 2000 \text{ kg} \cdot \text{m}^2).

Rotational Kinetic Energy Formula

  • Formula: (KE_{rot} = \frac{1}{2} I \omega^2).
  • Inputs:
    • (I = 2000)
    • (\omega = 36.65)
  • Result: Calculated rotational kinetic energy._

Translational Kinetic Energy of the Helicopter

Translational Speed Conversion

  • Helicopter speed: 80 miles per hour (mph).
  • Conversion to meters per second:
    • 1 km = 1000 m, 1 hour = 3600 seconds.
    • Result: 22.22 m/s.

Translational Kinetic Energy Formula

  • Formula: (KE_{trans} = \frac{1}{2} MV^2).
  • Inputs:
    • Mass (M) = 200 kg
    • Speed (V) = 22.22 m/s
  • Result: Calculated translational kinetic energy._

Total Kinetic Energy

  • Total kinetic energy = Rotational kinetic energy + Translational kinetic energy.

Comparison of Kinetic Energies

  • Ratio of rotational to translational kinetic energy: 4.53.
  • Interpretation: Rotational kinetic energy is 4.5 times greater than translational kinetic energy.
  • Conclusion: The blades have significantly more rotational kinetic energy than the translational kinetic energy of the entire helicopter.

Conclusion

  • Summary of findings.
  • Encouragement to ask questions and engage with the lecture content.
  • Reminder to like, share, and subscribe to the channel.

Full transcript