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I know that there are a lot of questions in just the title itself. I'd appreciate it , if you guys could answer for atleast one of them.

Here's the exact scenario that's running in my head.

imagine a drone is loosely tied to a pole and it's trying to move forward but instead, it ends up revolving around the pole. This seems to be a usual torque problem if we consider the displacement and the force vectors.

but there is also another vector over here. ie. the tension force.

the tension force is acting upon the drone exactly perpendicular to the tangential force. can we cross-product these two force vectors?

if yes, then what will the result vector be? is it torque and if it is torque is this the reason why the earth rotates while revolving around the sun?

if no, then why? and what is the condition to be considered before doing the cross product? why were we able to use the cross-product when it was displacement against force vectors and why are we not using the cross-product when its force against force?

kevin godfrey
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  • Sorry but I don’t get it. You don’t get to choose if you need to use a cross product. The torque is defined via $\tau=\vec r\times \vec F$. – ZeroTheHero Apr 18 '20 at 05:07
  • okay putting the torque aside, what will be the cross product of those two force vectors? – kevin godfrey Apr 18 '20 at 05:15
  • The cross product (or any product) between two forces has no physical meaning. – John Alexiou Apr 18 '20 at 06:47
  • Related: https://physics.stackexchange.com/a/516069/392 – John Alexiou Apr 18 '20 at 06:47
  • why? Just because you use a cross product in the calculation for torque, does not mean that every cross product is a torque. There are other uses for the cross product, all of which involve something of the form $$\text{(position)} \times \text{(something)}$$ – John Alexiou Apr 18 '20 at 07:00
  • yes, I agree with the point that every cross product is not a torque. but what if the forces are at a distance, opposite and they are attached to each other wouldn't that result a torque at some point of their attachment – kevin godfrey Apr 18 '20 at 07:02
  • I would like to think torque as a result of two or more forces acting at a point at some unit of distance. like if we take the example of a door, think the hinge as a resisting force acting opposite to direction of the applied force so that the door doesn't come of in the direction of the applied force. – kevin godfrey Apr 18 '20 at 07:10
  • imagine two water sources flowing in the opposite direction but side by side. now at the point of contact, we expect to see a whirlpool(little one atleast) but what if the same water sources travelling in the opposite direction come face to face, they'd just cancel each other right. – kevin godfrey Apr 18 '20 at 07:28
  • thus I starting to think that torque is a result of two opposite forces acting at a distance. – kevin godfrey Apr 18 '20 at 07:34
  • anyway, we are going way off the topic over here. the first and foremost question was when do we know that we do a cross product on two vectors and when do we realize that we do not apply the cross product? we certainly didn't think when we used the cross product on a distance and a force vector , as there was a true observable phenomenon associated with it, so id like to believe that there are other phenomenons that may or may not be observable but very real and discoverable with this concept – kevin godfrey Apr 18 '20 at 07:49

1 Answers1

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Yes, we can take the cross product of two vectors, nothing stops us. The question you are asking is like asking whether I can add any two real numbers, the answer to which is yes because real addition is an operation defined for two real numbers to give another real number. Similarly, cross product is an operation to give a vector from two any vectors. But we don’t take cross product of forces because it doesn’t yield a physical quantity of importance (as far as I know!).

EDIT to answer the edited question: No, the reason Earth rotates is not what you have suspected in the question. The sun is only responsible for the revolution of Earth. As for the rotation, it has to do with how things form in space (universe); the property of rotation comes about due to the way it is formed.

ModCon
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  • I disagree with your first paragraph. The tangential force on the drone has a non-zero torque about the location of the pole, and hence will describe its angular acceleration about the pole. – BioPhysicist Apr 18 '20 at 04:51
  • @Aaron Stevens Oh okay, I have removed the first paragraph from my answer. Could you please explain why this is so? Because the torque is acting on the pole and not on drone. – ModCon Apr 18 '20 at 04:59
  • The force acting on the drone has a torque about the location of the pole. This is similar, say, to pushing open a door by applying a force to the edge of the door. The force you apply has a torque about the hinge. – BioPhysicist Apr 18 '20 at 05:02
  • I think I get it now. So this is same as rotation about a fixed axis outside the rigid body right? I really messed up here and this is actually a pure rotation problem. Thank you for pointing this out! – ModCon Apr 18 '20 at 05:08