Rotating aircraft

I guess a lot of you will have seen this video of the crash at JFK airport this week.

It’s almost a perfect example of what I’ve recently covered in my dynamics class, concerning collisions that result in things spinning, because the forces don’t act through the centre of mass. So, in this example, the impulse due to the collision of the wing of the A380 on the tail of the smaller plane sends the smaller plane spinning. (A full analysis of forces is complicated here due to friction between the wheels of the small plane and the ground).

I wouldn’t have liked to be on the spinning plane.  I’m not sure what model it is, but I’m guessing it’s about 25 or 30 metres long. That would mean people at ends of the cabin would be around 10 m or so from the centre of mass (the axis of rotation).  The film shows it turns about 60 degress in around a second, or approximately 1 radian per second. So a quick application of our centripetal force equation angular velocity squared times radius gives us an acceleration (towards the axis of rotation) of around 10 metres per second squared.

That’s the same as the acceleration due to gravity, or ‘1G’. A roller-coaster ride. But what would be bigger would be the initial acceleration at the point of impact. This one’s a touch harder to estimate, but the plane probably get’s up to 1 radian a second rotation rate in about a quarter of a second, giving an initial azimuthal acceleration (azimuthal being in the direction around the axis of rotation) of more like 40 metres per second squared, or 4 G.

If you were standing up at the time, you wouldn’t be afterwards.

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