Why do charged objects attract pieces of paper, but not pieces of metal? I do not understand one concept in Physics: why charged objects (eg. a charged rod or comb) attract pieces of paper when brought close to them, but do not attract pieces of metal. 
I know that the pieces of paper are being polarized. But don't the pieces of metal have a sea of electrons which can move about, hence forming an electric field between the charged object and the metal?
Hope my doubt will be clarified.
Thanks
 A: You can attract metal with static electricity. Consider the text-book example of a conducting sphere vs. a dielectric sphere in an electric field.
Let's assume the field is homogeneous. This field polarizes both spheres, but in different ways:


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*Conducting sphere: The free electrons rearrange themselves on the surface until the total electric field is orthogonal to the surface. Overall this leads to a polarization of the sphere.

*Dielectric sphere: The electrons of all atoms of the sphere are tugged a bit away from their nuclii. This leads to a polarization of each atom inside the bulk material, but the individual dipoles cancel each other on the inside. Only those next to the surface don't cancel each other, and the whole thing "looks" like a surface charge. In total, this leads to a polarization of the sphere that is similar to the polarization of the conducting sphere, but always a bit lower, because the charges aren't as free to move as on a conductor.


The net force on the spheres inside a homogeneous field is of course zero, because dipoles aren't attracted by homogeneous fields: The forces on the positively charged regions cancel the forces on the negatively charged regions, except for maybe a torque on the dipole. Since the dipole of the conducting sphere or the dielectric sphere is induced, the dipole is already aligned, so there is no torque.
Dipoles are instead attracted by the change of the electric field. Mathematically speaking, the force is given by $\vec{F} = \vec{\nabla} (\vec{p}\vec{E})$. Because the induced dipole self-aligns with the external field, this always pulls the spheres into the field. 
To calculate the force that a nonhomogeneous field exerts on our conducting or dielectric sphere, you could try to decompose the field into an "average" homogeneous field that induces a dipole + an inhomogeneous field that pulls on the dipole. But that only works for inhomogeneities that are small across the sphere, when compared to the main field. 
The conducting vs. dielectric sphere model is only a toy model, but it shows that metal is actually attracted more strongly by static electric fields than paper, because its charges can move more freely.
Below is a very non-scientific experiment to show that metal is attracted by static electricity. It uses a small Van de Graaff generator that is built-into a "magic stick" and sold as a toy. (These are fun to play around with and also useful for science demonstrations. I highly recommend this type of toy, but I have no experience with the specific product that I linked to.) 
However, since electrons are free to move inside the metal, there are some practical differenes between using paper flakes and small pieces of metal:


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*Metal is heavier than paper, so you need thin pieces to be able to lift them up. Small bits of metallized film work well.

*Once you touch them in mid-air with your high-voltage electrode, they become charged and are repelled by the electrode. (This is the fun part of the toy). But as soon as they come near a non-conducting surface, they cling to it (through electrostatic induction) until they are discharged.  


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*The toy has a mildly-conductive coating to transfer charges from the high-voltage side to the metal. Using a comb does not work well for transferring the charges, because its surface is non conducting.


*Thin metal pieces typically have sharp edges. Since the metal is a equipotential surface, the electric field can become quite large at these edges. This leads to a weak corona discharge that sprays charges onto the comb, which effectively discharges it. This problem is more severe when the air is humid. Electrostatic experiments are best done indoors when its cold outside, because then the humidity in the room is (usually) low.  


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*Maybe this explains why your metal pieces didn't move?



Here is a quick try with the "magic wand" and paper (standard 80g/m^2, which is a bit too heavy). Ballpoint pen for scale, and for my cell-phone-camera to focus on.

Here is mylar foil, for comparison:

I used a piece of paper as the bottom surface, because it can actually accept charges from the metal pieces. This avoids the problem of the clinginess of the metal pieces. However, the paper surface charges up and repels the metal pieces again, and you get a very pronounced boune-back-and-forth effect. As the paper surface gets more and more charged, the mylar pieces move more and more out. You can see this a bit more clearly in the longer video. Note how the metal pieces move away from the paper, but cling to the table.
I have to admit that I am not entirely sure I understand the clinginess phenomenon. I think it is a complicated mix of the triboelectric series, grounded planes with isolated surfaces, and induced dipoles in the mylar film. But in my experience this is typical for electrostatics: Any real world application of electrostatics is about an order of magnitude more difficult than you initially think.
A: The fact is that metals do get polarized but in a different way. Since electrons are rather free, they distribute themselves along the frontier of the system, being attracted by the field. But they do so in such a way that the field becomes zero inside the metal, because the contribution from the external field and these electrons cancel each other.
You could picture this in a different way, metals have some kind of "electric plasticity", by which I mean they can change their charge distribution and this prevents them moving as a rigid body. This is similar to pushing some material that has some plasticity like clay: it does not move as whole when you push it, like a rigid solid would, but instead it deforms and the applied force is distributed internally in a way that the clay as a whole does not move because is not affected by the force. But in this analogy metals would be a special type of clay that recovers its shape (charge distribution in the metal) after the field disappears, more like jelly.

Update from comments...
Of course the metal will move if the electrical field is sufficiently strong. What I have just explained applies when comparing small pieces of paper with electron excess and similar pieces of metal in equal conditions or not charged at all.

A: Charged objects attract both metal and paper, in fact they will attract metal more due to the delocalised electrons as opposed to electrons just repelling or attracting within their shells, as the latter doesn't induce charges, but just distorts them.
