Question

An airplane of mass flies horizontally at an altitude of 10 km with a constant speed of 250 m/s relative to Earth. (a) What is the magnitude of the airplane’s angular momentum relative to a ground observer directly below the plane? (b) Does the angular momentum change as the airplane flies along a constant altitude?

Answer 1

The magnitude of the airplane's angular momentum is 1.0 × 1011 kg·m2/s for an airplane flying at 10 km altitude and at a constant speed of 250 m/s. Angular momentum remains constant as long as the airplane maintains a constant altitude and speed.

Step-by-step explanation:

Angular Momentum of an Airplane

To answer the student's question regarding an airplane of mass 4.0 × 104 kg flying at a constant speed of 250 m/s at an altitude of 10 km:

1. Angular momentum (L) relative to a ground observer directly below the plane is given by L = mvr, where m is the mass of the airplane, v is its velocity, and r is the radius of the circular path above the observer. Here, r = altitude = 10,000 m, therefore L = (4.0 × 104 kg) × (250 m/s) × (10,000 m) = 1.0 × 1011 kg·m2/s.
2. As the airplane flies along a constant altitude with a constant speed, the angular momentum remains constant because the radius and the velocity (magnitude and direction) of the airplane stay the same relative to the observer.

The magnitudes of the mass, velocity, radius, and the resulting angular momentum provide insight into the conservation of angular momentum in this context.