Rotation around center of mass question

In summary, the question being discussed is why an object's motion can be viewed as a translation of its center of mass and a rotation around it. It is argued that this makes sense because the center of mass acts as a point particle subject to external forces, while the rotational part of the motion is caused by internal forces. However, it is questioned why an object must rotate at all, and it is explained that this is a result of conservation of angular momentum. It is also noted that this concept of rotation only applies to rigid bodies and is an abstraction based on observations in physics.
  • #1
aaaa202
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I had quite a few posts about this some weeks ago, but I am still not sure about it. My question is about why you can always view the motion of an object as a traslation of the cm and a rotation around it. It makes sense in the light of the cm being the point which moves as a point particle only subject to external forces. But then that must mean that what causes the rotational part of the motion is purely internal forces. Is it then so that the sum of all the internal forces causing the rotation is zero with respect to an inertial frame of reference?
Hope it made at least somewhat sense..
 
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  • #2
Why do you think external forces can only produce a translation of the center of mass? Certainly external forces can produce a rotation as well, as long as there is a net torque.

However, in the case the net external force is applied at the center of mass (e.g. in the case of gravity), there is indeed no net torque. In that case, the rotations of the object are due to purely inertial motions (i.e. it's initial conditions contained rotations).

The motion is then a solution to the torque free Euler's equations.
 
  • #3
You can not consider the internal forces in determining the motion of the object. The motion of the object is only due to the external forces. What makes you think that the external forces do not cause the rotation?
 
  • #4
Well if you look at a point on a stick rotating then that point is moving in a loopy path, so surely internal forces must be present in making it move like that? Had it only been external forces then the point would move in a specific direction. Thus it must be at least a combination of internal and external forces that produces a rotation.
So can someone explain to me how a rotation is caused in terms of internal and external forces. I know what a torque is and all that. What I find hard to grasp is the fact that nothing in nature dictates that an object MUST rotate. You can say: I know the center of mass will move in a straight line. Also you know that it is geometrically possible for an object to rotate about a fixed point. But what law in nature says that it MUST do so. As soon as it rotates, then yes, you can identify the rotating part of the motion, calculate the work done it and then find out the angular velocity, acceleration and so forth. But that is only after you have accepted the fact that a rotation exists as a phenomenon in nature and not just a solution to the equations of motion.
 
  • #5
If there is no external force, than a rigid body can only move in a straight line with constant velocity and/or spin with constant angular velocity about its center of mass. Why about the center of mass? Because the center of mass of any system of material points (e.g., a rigid body) with no external forces must move in a straight line; this easily follows from Newton's laws.

If there is an external system of forces, then the body can move and rotate in just about any way. The center of mass might simplify the analysis in certain cases, but not always.

A common case, however, is motion under gravity, with an important subcase where gravity is uniform. This system of forces does not produce any net torque, so the spin of the body, if any, is unaffected by it. So it is common to say that gravity is applied at the center of mass only; but that's a simplification valid only for a uniform field of force.
 
  • #6
The laws of nature are based off of observations we have made about certain phenomenon. For example Newton established his laws by observation and one of them concluded that F=dp/dt and by extension F=ma. By the same token, we have established rotational analogues for kinetics and kinematics and for that we have the rotational analogue of torque, τ=dL/dt and by extension τ=Iα=r x F. It's accepting that rotation is another behavior we attempt to describe with mathematics.
 
  • #7
aaaa202 said:
Well if you look at a point on a stick rotating then that point is moving in a loopy path, so surely internal forces must be present in making it move like that? Had it only been external forces then the point would move in a specific direction. Thus it must be at least a combination of internal and external forces that produces a rotation.
So can someone explain to me how a rotation is caused in terms of internal and external forces. I know what a torque is and all that. What I find hard to grasp is the fact that nothing in nature dictates that an object MUST rotate. You can say: I know the center of mass will move in a straight line. Also you know that it is geometrically possible for an object to rotate about a fixed point. But what law in nature says that it MUST do so. As soon as it rotates, then yes, you can identify the rotating part of the motion, calculate the work done it and then find out the angular velocity, acceleration and so forth. But that is only after you have accepted the fact that a rotation exists as a phenomenon in nature and not just a solution to the equations of motion.

Basically conservation of angular momentum says something that is rotating initially must remain rotating unless there is external torques. Of course, one may then ask "why is there conservation of angular momentum?" To which physics can only say basically "because that is what experiment shows".
 
  • #8
Rotation as a phenomenon distinct from translation exists only for "rigid bodies". These are abstractions, so one could speculate that rotation does not exist as a natural phenomenon. Indeed, at the microscopic level (but ignoring quantum mechanical effects), atoms just move along some path, which is curved due to interaction with other atoms.

The force of this interaction is quite large, but finite in real bodies. This sets a limit to the ability of a real body to rotate. Beyond a certain value of angular speed, a body cannot exist as a single body, because the force of interaction is not strong enough to bend the trajectories of its atoms to hold them together. No such limit exists for translation (the speed of light sets another limit, though).
 

1. How does rotation around the center of mass affect an object's stability?

Rotation around the center of mass can affect an object's stability by changing the distribution of its weight. If an object's center of mass is located above its base of support, it will be more stable. However, if the center of mass is outside of the object's base of support, it will be less stable and may topple over.

2. What is the difference between rotation and revolution?

Rotation refers to the movement of an object around its own axis, while revolution refers to the movement of an object around an external axis. For example, the Earth rotates around its own axis, but it also revolves around the sun.

3. How does the distribution of mass affect a rotating object?

The distribution of mass can affect a rotating object by changing its moment of inertia. Objects with more mass distributed further from the center of rotation will have a larger moment of inertia and require more torque to rotate, while objects with less mass distributed closer to the center of rotation will have a smaller moment of inertia and require less torque.

4. Can an object rotate around its center of mass?

Yes, an object can rotate around its center of mass as long as it is not affected by any external torques. This is known as a pure rotation, where all points on the object move in circular paths around the center of mass.

5. How does the position of the center of mass affect an object's rotation?

The position of the center of mass affects an object's rotation by determining the point around which the object will rotate. If the center of mass is located closer to one end of the object, it will rotate around that end. However, if the center of mass is located in the center of the object, it will rotate around that point.

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