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Suppose force is applied to an end of a rod in a perpendicular direction of the rod which is resting on a frictionless surface( for example: frictionless surface of a table). It is supposed to rotate. Why will that rod rotate?

To be honest I really do not understand why does it rotate in such cases. It would be a great help if anyone provides me a link or explains me this thing.

MSKB
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  • What do you mean by an "elongated" rod? How exactly is the force applied to the end of the rod"? Parallel to the horizontal frictionless surface and perpendicular to the rod? We need more details. – Bob D Mar 26 '21 at 14:56
  • I edited the question. Hope that now it will be clear. – MSKB Mar 26 '21 at 15:05

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It will rotate as well as translate because the force is not applied to the center of mass and there are no other forces (except gravity, which is downward) acting on the rod. If the force was applied to the center of mass of the rod (presumed to be at the center of the rod if its mass is uniformly distributed along it length), then the rod will only translate and not rotate.

As you explained that for the case stated in the question the rod will translate and rotate, it would be a little bit more helpful for me if you could explain why does it rotate.

See the diagram below.

For the purpose of determining rotation, the center of mass of the rod can be considered mid point of its length (assuming its mass is uniformly distributed along its length.

You can see there is a net torque of $\tau=FL/2$ about the center of mass which will initiate clockwise rotation rotation of the rod. The force $F$, which is unopposed, will also result in translation of the COM. If the line of action of the force was through the COM, there would be no net torque on the rod and its motion would only be translation.

Hope this helps.

enter image description here

Bob D
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  • As you explained that for the case stated in the question the rod will translate and rotate, it would be a little bit more helpful for me if you could explain why does it rotate. – MSKB Mar 26 '21 at 15:17
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    Sure. I'll update my answer in a little while. – Bob D Mar 26 '21 at 15:23
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    @MohammadSakibShahriar See update to my answer. – Bob D Mar 26 '21 at 16:13
  • Sir will the center of mass translate in a limear path? – MSKB Mar 26 '21 at 17:20
  • Excellent question. What do you think will happen? – Bob D Mar 26 '21 at 17:30
  • I think it should be linear – MSKB Mar 26 '21 at 18:58
  • @MohammadSakibShahriar It really depends on how and for how long the force is applied. If it is applied like I showed it but only momentarily (like a brief impact), the the rod will rotate at constant angular velocity around the COM and the COM will move linearly and at constant velocity after a brief acceleration. But what do you think would happen if the force was constant with no change in direction and attached to the end of the rod (say by a frictionless pin)? – Bob D Mar 26 '21 at 19:10
  • Then COM will at first align with the direction of applid force and then it will move in a linear path..therefore if we draw the path it will be something like the curve of e^x...is ths assumption correct? – MSKB Mar 26 '21 at 19:12
  • @MohammadSakibShahriar Hmm. What about conservation of angular momentum. Won't the COM continue to rotate but about the point of application of the applied force after the rod aligns with the force? In other words, won't there will be both rotation of the rod about the center of mass and rotation of the center of mass of the rod about the point of application of the force? What do you think? – Bob D Mar 26 '21 at 19:50
  • If we are using our hand to apply the force constantly then it will turn out that the required forces which usually evolve if the force was momentary will be nullified or neutralized or stabilized but if we think of an hypothetical thing apply force constantly then i guess the whole system will rotate and their axis of rotation might not remain the same.....this is what I think.....I know this thought isn't correct for about 99%...looking forward to learn more. – MSKB Mar 26 '21 at 19:58