Something I don’t quite understand from a physics standpoint. Imagine a car going down a road approaching a roundabout, on neutral; it can follow the roundabout 180 degrees and start going in the reverse direction while only losing a little speed/energy. But the car did a lot of “work” in the physics sense — a multi-thousand-pound vehicle completely reversed direction in a few seconds. How is that energy redistributed (force diagram, etc) to show where the energy for all that work came from?
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The main force is applied perpendicularly to the movement, so no work is actually done. You’re basically deflecting the velocity, not really changing it, in a simplified model.
Mind you, in real life, there are a ton of factors screwing everything up, including how the rubber on the wheels behave, as well as the differential, plus a bunch of elasticity eveywhere.
Firstly, as was mentioned, there’s no physics-work done if the acceleration is perpendicular to the movement, which is what happens when you go in a circle.
Secondly, the energy doesn’t go anywhere in an idealized setup, because energy isn’t a vector quantity. A car going the same speed in the opposite direction still has the same kinetic energy.
If you’re looking for where the momentum went, there’s a force exerted on the road by the tires to keep the car going in a circle. The force on the car is toward the center of the circle, like the orbit of a moon or when you swing a mass on a string. So the road and the planet it’s attached to will have their momentum changed very slightly in the opposite direction.
Imagine a ball swinging on a string. Obviously no work is done, since it is easy to keep the ball swinging. The car is the ball.
The energy before and after is the same – while speed comes with a direction energy does not. If the force on it pushes sideways, neither speeding it up nor slowing it down, then no work is done.
It loses quite a lot of energy and speed. The straighter the line the less speed you lose. The more change to the line you introduce the more speed will be shed. The lateral forces exerted on the car during turns and moves is where the speed is lost. I would also add that you have ‘circled back’ rather than reversed direction. The energy for all that ‘work’ was present at the starting conditions. The loss in speed post-turn is dependant on the traction and amount of directional change.