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In the following image, we have two objects (I'm not sure whether to call them beams, rods, shafts, or axles) connected by a frictionless joint (I think it's a pinned joint, but not sure).

The blue surface is frictionless.

Figure

A constant force, F, is applied at point A, and as the red object rotates around point J, the direction of the force is always perpendicular to the axis of the red object, so there is no component of force that acts along the length of the object (I think another way of saying this is that there is no axial force, but I'm not sure).

Assume that the red and green objects have uniform density, and have equal mass.

My question is this:

Will all the force be expressed as torque around J? Or will some of the force cause the entire contraption to move rightwards along the blue frictionless surface?

My gut tells me that all of it will be expressed as torque, but I can't convince myself why this is the case.

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Your gut is wrong.

There is just one horizontal force acting on the two beams. That means the center of gravity of the beams will accelerate to the right, because that's how Newton's Laws work...

The center of mass will accelerate as though all the forces acting on the object act on the center of mass

Then you separately worry about rotation, based on inertia, moments, etc.

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  • $\begingroup$ Thank you, I think I should re-read chapters 18 and 19 of Feynman Lectures on Physics, Vol 1, in order to better convince myself of the very useful proposition you have just stated. $\endgroup$ – spacediver Dec 6 '16 at 23:53
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Will all the force be expressed as torque around J?

You can always take a force and an axis and determine if that force contributes to a force around that axis. That doesn't mean that the axis is fixed, though.

Or will some of the force cause the entire contraption to move rightwards along the blue frictionless surface?

Forces aren't split between generating torque and generating acceleration. All of the force can contribute to a torque and all of the force will contribute to the acceleration of the (center of mass) of the object.

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