I noticed in this recent video that some of the passengers are not wearing their seat belts. I realize this is not a typical commercial flight, but is it advisable to wear seat belts when a 747 or similar aircraft is flying so close to the ground, (apparently) during a final approach? Or are the safety precautions here so thorough that it's not actually necessary in this case?
It is, of course, advisable to wear your seat belt, yes. However, there appears to be somewhat of a tradition of not always wearing seat belts on Air Force One:
Stanley B. Greenberg, Dispatches from the War Room: In the Trenches with Five Extraordinary Leaders (Google Books):
Nobody wears seat belts and everyone uses their cell phones while the plane is taking off.
Presumably the crew would provide a special warning if they expected a rough ride.
Yes, it is always advisable for passengers to wear the provided safety belts in all phases of flight. This is especially true for aircraft on takeoff, landing, in low level flight, or in any other flight regimes that are especially prone to turbulence or other risk exposure.
A large, heavy aircraft—such as a B747—will be less affected by wake or mechanical turbulence than would a smaller aircraft—such as a CRJ200 or a C172. However, even large, heavy aircraft can be subjected to severe turbulence that could result in injury or death if passengers are not restrained by appropriate safety belts.
Additionally, for flights conducted under 14 CFR 121—which I am confident is a majority of the US operated passenger flights involving the B747 (though not, obviously, Air Force One pictured in the question above)—passengers are generally required to:
occupy an approved seat or berth with a separate safety belt properly secured about him or her during movement on the surface, takeoff, and landing
Excerpted from 14 CFR 121.311 (b)
Don't worry about what Obama does in particular . It's always advised to wear seat belt whether you are in Boeing 747 or other small planes.
According to this Telegraph.co.uk article:
"Seat belts are required and designed to ensure passenger safety and reduce the risk of injury, particularly during deceleration, turbulence and unplanned or difficult to predict events.”
And later on in the same article:
Last year, severe turbulence caused three EasyJet crew members to “hit the ceiling” over Italy, according to a passenger eye-witness, with one sustaining a hip injury.
Now all that can be said is if you don't want to be next victim wear the seatbelts.