Like other loose objects, air molecules in the car get forced to the left increasing the air density on that side. The greater air density on the left displaces the lower density helium balloon to the right.
Another way of understanding the situation is to remember the equivalence Einstein explained between gravitational and inertial forces. An accelerating car (turning to the right) produces the temporary equivalent of another gravitational field pointing to the left. That is why most objects want to move in that direction. The helium balloon, however, responds to that equivalent field just as it does to Earth's gravitation, moving in the opposite direction.
Answered by: Paul Walorski, B.A., Part-time Physics/Astronomy Instructor
The law of buoyancy, discovered by Archimedes, basically says that any material or object immersed in a fluid (and air) will tend to rise through the fluid if the fluid density is greater than the material density.
Because the density of a balloon full of helium is less than that of air, we normally see a helium balloon moving from a place from where it is more dense (towards the Earthï¿½s surface) to a place where it is less dense (away from the Earthï¿½s surface.)
In this example when a car is making a right turn, consider also Newton's first law of inertia, an object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force. It is the natural tendency of objects to keep on doing what they're doing. When you are driving down the road, the air molecules in the carï¿½s compartment move at the same speed and direction the car is moving. Suddenly you turn to the right, and the molecules tend to travel in the same direction that they were going, straight. More molecules now build up on the left side of the car; the air is now denser on the left than it is on the right.
With the air more dense on the left than on the right, the helium balloon will tend to move from where it is more dense (the left) to where it is less dense (the right.)
Answered by: John Bentler, Pre-engineering, Highline College, Midway WA
As the pressure builds up in this region, the molecules start to accelerate to the right due to a net force from their left. This force is proportional to the volume occupied by the object (= surface area along pressure gradient x pressure difference). Therefore the acceleration of an object due to this pressure difference is propotional to the volume / mass (1 / density). This analysis leads to the intuitive result that the densist objects accumulate at the wall of the car.
Often the force imparted by a turning object is refered to as G force (like in rollercoasters and fighter jets) because its effect is indistinguishable from gravity. A helium balloon rises in air because, although it is attracted to the centre of gravity, the denser air is attracted more strongly. In the car the denser air will accumulate at the left side of the car, forcing the helium balloon to the right.
Answered by: Stuart Taylor, Chemistry graduate student, Oxford