# Rotation around center of mass question

aaaa202
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..

Gold Member
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.

cmmcnamara
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?

aaaa202
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.

voko
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.

cmmcnamara
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.