Calculating Angular Momentum of an Aircraft Near Pittsburgh

[tony873004]

An aircraft of mass 10,000 kg is 100 km northwest of Pittsburgh at an altitude of 3000 m flying due east at 300 km/h. What is its angular momentum about Pittsburgh?

L=rp sin theta

for r, would I use 100 km (converted to m)
Or the closest approach to pittsburgh, which would be cos(45*300km/h)

For velocity in computing p, would I use 300 km/h (converted to m/s) or only its radial component to pittsburgh which is 300 / sin 45

 

[OlderDan]

There are lots of ways to approach this. You just have to be consistent. r*sin theta should be the same wherever you calculate it. The radial component of p would not contribute to the angular momentum

 

[thepatientmental]

In this scenario, the angular momentum of the aircraft about Pittsburgh can be calculated using the formula L = rp sin theta, where r is the distance from Pittsburgh to the aircraft, p is the linear momentum of the aircraft, and theta is the angle between the r vector and the p vector.

For the distance component, we would use the closest approach to Pittsburgh, which is 100 km (converted to 100,000 m). This is because the angular momentum is measured from the point of reference, which in this case is Pittsburgh.

For the velocity component, we would use the radial component of the aircraft's velocity, which is 300 km/h (converted to 83.33 m/s). This is because the angular momentum is a vector quantity and only the component of velocity in the direction of the r vector is considered.

Using these values, we can calculate the angular momentum of the aircraft about Pittsburgh as:

L = (100,000 m) * (10,000 kg) * (83.33 m/s) * sin(90°)

= 8.33 x 10^11 kg*m^2/s

Therefore, the angular momentum of the aircraft about Pittsburgh is 8.33 x 10^11 kg*m^2/s. This value represents the rotational motion of the aircraft around Pittsburgh, taking into account its mass, distance, and velocity.