Is the answer 7? The number of degrees of freedom of a system can be viewed as the minimum number of coordinates required to specify a configuration. Applying this definition, we have:

  • For a single particle in a plane two coordinates define its location so it has two degrees of freedom.
  • A single particle in space requires three coordinates so it has three degrees of freedom.
  • Two particles in space have a combined six degrees of freedom.
  • If two particles in space are constrained to maintain a constant distance from each other, such as in the case of a diatomic molecule, then the six coordinates must satisfy a single constraint equation defined by the distance formula. This reduces the degrees of freedom of the system to five, because the distance formula can be used to solve for the remaining coordinate once the other five are specified.
  • 1
    $\begingroup$ Where did you get 7? $\endgroup$ – Mike Apr 6 '17 at 14:15
  • $\begingroup$ Can the insect move along the rod? Is there only one parameter specifying the location of the bug relative to the rod? $\endgroup$ – ja72 Apr 6 '17 at 14:34
  • $\begingroup$ Obviously, 3 coordinates locate a point in space, but are additional specifications required to indicate rotation (or lack thereof)? $\endgroup$ – David White Aug 7 '17 at 17:01
  • $\begingroup$ Can the insect walk around the rod? Does the rod have ends, or is it an infinite line? $\endgroup$ – ja72 Aug 7 '17 at 20:11

The answer depends on interpreting the question. But my answer would be three, because it can (1) rotate in one spot, it can (2) move along the rod, and it can (3) move around the rod.

An insect typically has six segmented legs, four wings, and various other moving body parts. All those involve several degrees of freedom, so if you include them in your count, your answer will be a lot. Presumably, you're supposed to ignore all those degrees of freedom, and consider the insect as a more rigid object.

Now, think of the insect as a rigid body, but one that is able to move around. It could maybe go up on its hind legs, for example, which would be another degree of freedom that I didn't list above. But I tend to think that you're supposed to just imagine the insect walking around in the most boring way possible. That involves just walking anywhere on the rod (two degrees of freedom because the rod's surface is two dimensional), or turning around in one spot (one degree of freedom because it just takes one angle to say which way the insect is pointing). That adds up to three.

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    $\begingroup$ I think this answer is correct, although I would tend to ignore (1) and view the insect as a pointlike object. $\endgroup$ – Noldig Apr 6 '17 at 14:33
  • $\begingroup$ Yeah, that's another reasonable interpretation. And it seems @ja72 might also ignore (3), which is yet another. It just comes down to opinion... in my opinion. :) $\endgroup$ – Mike Apr 6 '17 at 15:13

The answer is 7. The number of degree of freedom of rod in space is 6 and the degree of freedom of insect is 1, also consider that the rod is rigid.


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