Physics Question #9298

Andre Depre, a 64 year old male from Tienen, Belgium asks on March 1, 2016,

Can centrifugal force be used to create an inertia drive by tightening/pulling the orbiting object towards the center on one side of its orbit and then lighten/release the object on the opposite side?

As the center (with 1000s rpm spinning motor) pulls the orbiting object in, at the same time the center is, of course, also pulled forwards in the direction of the orbiting object. And when the orbiting object is then lightened/released on the opposite side of the orbit, this causes the center even more to move towards the point where the orbiting object was originally pulled in.

My idea is that all it takes is a bit of synchronization between the spinning engine and the second engine that pulls in and releases the object at the opposite points in its orbit. Can this make inertia drive possible and, if so, what magnitude of force are we talking about? Probably not enough to lift an object into space, but perhaps it can be used in space itself.

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The answer

Jess Brewer answered on March 4, 2016

This is a cute problem, and if you don't think about it the right way it almost seems like it should work. I started thinking in terms of impulses and tension changes etc. and got pretty confused before I went back to basics.

The only forces acting on the two masses (you and the tether ball) are the tension force acting on the ball and the equal and opposite tension force acting on you.  These are both centripetal (i.e. toward the centre of mass, which lies on the rope near your end).

Therefore the centre of mass of the system has no net external force acting on it, so if it's initially at rest, it stays at rest.  If the centre of mass stays put, so do you, on average.  QED.  You do continue to orbit around the centre of mass, but it stays put.

[EDITOR: To summarize: We can ignore whatever is on one end of the string or the other, just consider the overall centre of mass of the system, which is someplace in the middle of the string, closer to the heavier of the two masses. If we simply focus on that point, after all the pulling in and letting out of rope, no matter where the various parts of the system are when you pull in or let out, that centre of mass point (on average) won’t be moving anywhere and this is simply due to Newton’s laws of motion.]

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