# Why do objects always rotate about their centre of mass?

wrobel
Summary:: Conceptual question on rotation.

Why do unconstrained objects always rotate about the lines passing through their CMs when tangential forces are applied to them? I understand that if an object does not rotate about its CM, th
1) a free rigid body is not obliged to have a fixed axis of rotation;
2) instantaneous axis of rotation is not obliged to pass through the center of mass.
All these things can change from one inertial frame to another one.

vanhees71, A.T. and etotheipi
a free rigid body is not obliged to have a fixed axis of rotation;
Can you please explain what this means?
instantaneous axis of rotation is not obliged to pass through the center of mass.
Why? Can you give me a proof?

jbriggs444
Homework Helper
Can you please explain what this means?
@wrobel is using a axis of rotation to mean the set of points on a rigid body that are instantaneously at rest in a given inertial frame of reference.

Consider, for instance, an ideal car wheel as the car rolls down the highway and use the frame of reference of the road. The axle is not instantaneously at rest. So it does not qualify as the axis of rotation in this sense.

The points that are at rest are at the contact patch of tire on road. So the "axis of rotation" as he uses the term would be the line of points running across the width of the tire where it meets the road. Obviously, this is only the axis of rotation for an instant. A little bit later the axis of rotation will be a new line a little bit further down the road.

You can see that if we changed to a frame of reference anchored to the car that the axis of rotation would then be at the axle.

vanhees71, wrobel, Leo Liu and 1 other person
etotheipi
Also, if we allow non-inertial frames, you could imagine a coordinate system with its origin fixed to a specific moving point on the tire, with axes always aligned with a coordinate system fixed in the road frame. The motion of the wheel in this frame is now restricted to rotations about this point, even though it is not the centre-of-mass!

vanhees71