2

If I push or hit an object in space (vacuum and no gravitation) in direction what is not going trough its centroid, will it rotate or move along in straight line?

I expect that on earth it will depend on what is less difficult for the object (rotation or linear movement). So the object will do some kind of combination of both movements (rotating and also moving along the direction of impulse or force).

But how could an object "decide" what to do in space, where is not resistance?

Qmechanic
  • 201,751
matousc
  • 123
  • "It" doesn't decide what to do. Physics decide what it "must" do. It is the same principle in vacuum. – Gonenc Feb 12 '16 at 08:41
  • @gonenc Thank you for making that clear. I thought that decision is only up to the object. – matousc Feb 12 '16 at 09:18
  • 4
    @gonenc : Physics decides nothing. Physics itself mean physical observation. We observed such motions, and explained it as physics. – Anubhav Goel Feb 12 '16 at 14:39

6 Answers6

10

Any linear force not going through the centre of mass will create torque, which I hope you know, is related to how far from the centre of mass the line of force is.

So, if you manage to hit the object exactly at its centre of mass, i.e. the line of force is directly passing through the centre of mass, then it will show NO ROTATION. It will go straight ahead in a line.

But, if you fail to do so, i.e. the line of force misses the centre of mass, it will show BOTH kind of motions, Rotational and Linear. It will go straight ahead in a line as in previous case, but will also rotate. How much is the speed of rotation depends on how badly you missed the centre of mass.

But in both cases, the total momentum will be (has to be) same.

AneesAhmed777
  • 228
5

If the line of action of the force is is not through the centre of mass you can transform the original force $\vec a$ by adding two forces $\vec a$ and $-\vec a$ (net force zero) acting at the centre of mass as shown below:

enter image description here

You can now consider these three forces as follows:

a force equal in magnitude and direction to the original force but passing through the centre of mass.
This force will produce a translational acceleration of the centre of mass of the object.

and

a pair forces equal in magnitude to the original force with one in the same direction as the original force and the the other one in the opposite direction.
This pair of forces is called a couple and produce a torque of $ax$ which is independent of any axis of rotation that you may choose.
A couple only produces rotational acceleration.

If the original force is through the centre of mass no couple is produced and so the object does not undergo rotational acceleration.

Farcher
  • 95,680
4

If you give a tangential force it would rotate. If you give a force at centroid, it will move in straight line. Along any other point, between tangent and centroid , it will show joint motion.

Splitting of force into tangential and along centroid will also depend on shape of object. Like you cannot give a pure rotation force to a rod which is not pivoted at any point and pivot is its momentary resting inertia. So it will both rotate and move forward even with just tangential force which will have a linear component as well. More is the mass concentrated at centre of mass more will rotaional component.

Anubhav Goel
  • 2,089
  • 1
    Why would the object not show joint motion when a tangential force is applied? The force will produce (temporarily) both linear and angular acceleration, giving the object both linear and angular velocity! I think this is a (small) correction... – FreezingFire Oct 10 '16 at 18:23
  • @FreezingFire Sorry! I don't think there is any linear acceleration when a pure tangential force is applied. Tangential component of any force leads to torque while linear component forward motion. When we say we apply tangential force, we mean no linear component. And hence, no linear motion. – Anubhav Goel Oct 11 '16 at 03:08
  • So you mean that if a rod resting on a table, not pivoted anywhere, is pushed at one of its ends, the force being perpendicular to the rod, then the rod will only rotate, and its centre of mass will not move? That wouldn't happen, and is easily proved. If this is not what you mean, then what do you mean? – FreezingFire Oct 11 '16 at 04:48
  • Yes, the rod would only rotate. If you Can you disprove it easily that I would appreciate that. – Anubhav Goel Oct 11 '16 at 04:56
  • The acceleration of centre of mass of any physical system is $\vec{F}/m$, where $\vec{F}$ is the net external force on the system, regardless of where the force is applied. Going back to my example, If the rod was pivoted at its centre, then the pivot would have to apply an equal and opposite force on the rod's centre of mass (CM) to keep the CM stationary. – FreezingFire Oct 11 '16 at 05:15
  • Net force here is 0. Since an equal and opposite couple is produced on other end. I still am not convinced. – Anubhav Goel Oct 11 '16 at 05:21
  • Let us continue this discussion in chat. – FreezingFire Oct 11 '16 at 05:46
  • 1
    -1. Unclear or incorrect. A tangential force causes both linear motion of the CM as well as rotation about the CM, the same as any other off-centre force "between tangent and centroid". Or perhaps when you say "tangential force" you mean a couple? – sammy gerbil Oct 18 '17 at 15:55
  • @sammygerbil Tangential force perpendicular to axis of object will always produce couple. Wont it? – Anubhav Goel Apr 04 '18 at 04:07
  • I agree with FreezingFire : any force applied off-centre will cause both rotation and linear motion. There is nothing special about the edge of the object. A force at the edge does not cause pure rotation. An off-centre force is equivalent to a couple and a force at the centre of mass. To produce pure rotation an equal and opposite force must be applied. – sammy gerbil Apr 04 '18 at 14:12
  • Hey Anuhbhav, a tangential force can only produce a couple if the object is pivoted. Otherwise, there is nothing to exert the normal force. Here, the object is floating so clearly its not pivoted. In the case of the floating object, the molecules in the object near the area where the force was applied will experience an immediate increase in velocity. This results in tension in the object. Ultimately, the molecules in the object will reach equilibrium as the momentum is evenly distributed among all the molecules. As such, the object will move linearly. Do correct me if I am wrong. – Luo Zeyuan Oct 22 '18 at 10:59
  • @LuoZeyuan I beleive inertia will act like pivot, otherwise why talking about rotational motion.... – Anubhav Goel Oct 23 '18 at 22:33
  • Yes, the rod will rotate, but the rotation is because initially, the molecules at one end of the rod is moving, whilst those at the other end is stationary. This is different from the case where force is applied at both ends of the rod because eventually, the rod will stop rotating. – Luo Zeyuan Oct 25 '18 at 01:29
  • I think the conservation of momentum can be used here. Consider the net momentum of a purely rotating disc. It has no net momentum, because the momentum of the individual molecules cancel out. So if the rod was to purely rotate when the force is applied, then clearly something is wrong because the momentum of what ever that applied the force was not conserved. – Luo Zeyuan Oct 25 '18 at 01:40
  • What I am considering is that,, translation motion occurs when a component of force is applied on centre of mass, since in tangential force no direct force is applied on centre of mass and I cannot see any component as well,, I am unable to get convinced... And few of my thought experiments abd real experiments are not allowing me this... – Anubhav Goel Oct 25 '18 at 01:46
  • @LuoZeyuan up... – Anubhav Goel Oct 25 '18 at 01:47
  • Maybe you can consider the rod as a collection of individual molecules. Then think about how the molecules interact when a force is applied on them. – Luo Zeyuan Oct 25 '18 at 01:49
  • If the force is applied on the centre of mass, then the molecules at the centre of mass will "pull" the molecules on either sides of the rod in the direction of the force. This is because the molecules are bonded chemically. If it was not applied on the the molecules there also "pull" the molecules next to them. – Luo Zeyuan Oct 25 '18 at 01:51
  • @LuoZeyuan I tried this analogy, but my experiment with a pencil are not consistent with this,, Other end of pencil always come back than starting line,, may be I will have to make a video to show my thought experiment... I will do it in later date,, I cannot get a mathematical solution to it at present as well... – Anubhav Goel Oct 25 '18 at 01:54
  • Did u try to rotate the pencil on a table? If so, then there's friction between the pencil and the table. The friction will act as a sort of pivot which results in rotation. – Luo Zeyuan Oct 25 '18 at 01:57
  • @LuoZeyuan But friction on each part is constant, acting more like inertia in space.. – Anubhav Goel Oct 25 '18 at 01:59
  • I think we should avoid extended conversation in comments and move to chat in above link.. – Anubhav Goel Oct 25 '18 at 02:00
  • If you consider your analogy and the conservation of momentum, then the molecules in the rod can only "pull" the nearby molecules in one direction, because momentum is conserved. So eventually, momentum will distribute itself evenly in the rod, and it starts to move linearly. – Luo Zeyuan Oct 25 '18 at 02:00
  • @LuoZeyuan No, like I said every next molecule due to its inertia, is acting like pivot here..causing only rotation.. – Anubhav Goel Oct 25 '18 at 02:02
  • Hmm... What if you consider your rod as a system of 2 molecules(Something like an oxygen molecule)? From what I can see, if you apply a tangential force on one of the molecules, the system does not rotate. – Luo Zeyuan Oct 25 '18 at 02:16
  • @LuoZeyuan Class time,,, talk to you later,, but two molecule analogy I tried but it failed,, in my thought experiment due to not being a tangent and in real due to fricton,,, – Anubhav Goel Oct 25 '18 at 02:23
1

If not influenced by any other forces then after pushing It will move in a straight line and most likely rotating as it goes. It would be real hard to push it without giving it some kind of rotation but it will always move in a straight line.

Bill Alsept
  • 4,043
0

If the net hitting force passes through the center of mass of the object being hit, it will have linear movement, otherwise, it will have some rotation as well as movement.

kpv
  • 4,509
0

If the line of action of the applied force is not through the "centroid" of the body (more appropriately the centre of mass, shortened as CM), then the body will both rotate and translate linearly.

What does this mean? Well, consider a wheel rolling on the road. If you focus your attention on the centre of the wheel (which, coincidentally, is also the CM of the wheel), you will see that it moves in a straight line. Any other particle on the wheel moves in complicated paths. This is the speciality of the centre of mass of a system, which moves in a straight line path in absence of a net external force on the system.

So now imagine you drive in a car alongside the wheel, and you adjust your speed so that the centre of the wheel appears to be stationary (just don't crash your car. It's precious). What you essentially did was move into a frame of reference having the same velocity as the wheel. Now if you look at the wheel, the wheel seems to be rotating about its centre! Whoa!

So you use this knowledge, and when you stop the car, you say that the wheel is both, translating (it's CM moves at a constant velocity), and rotating (in the frame of CM, the wheel is rotating). In fact, the above discussion applies to all bodies.

Now, when you apply a force not passing through the CM of the body, it has a torque about the CM of the body, and thus the force plays two roles. It not only accelerates the centre of mass, but it also gives angular acceleration to the body, that is, if you stick to the frame of centre of mass (here the frame is not inertial!), you will see that the body is rotating about the CM, but its angular velocity (rotational speed) is increasing, thus it has angular acceleration. All this ultimately means the body both translates, and rotates about the CM (although the "rotation" can be only seen properly in the frame of CM).

FreezingFire
  • 735