Suppose I have a rigid body, B, without any applied forces or moments. The
angular velocity of B is w. The inertial velocity of the center of mass is
zero.

Because there are no applied forces or moments, the angular momentum of B is
a constant.

Now, suppose my rigid body is instantaneously cut in two parts at time t = 1
sec, resulting in bodies B1 and B2.

1) Does conservation of angular momentum imply that the angular velocity of
B1 and B2 (about their respective mass centers) be equal to w at t = 1 sec?
How?

2) In general, will the mass centers of the two bodies, B1 and B2, separate
over time? Why?

3) Will the angular velocity of B1 and B2 remain equal to w if no external
forces or moments are applied to either body?

Thanks,
John

"John Lansberry" wrote in message ...
Suppose I have a rigid body, B, without any applied forces or moments. The
angular velocity of B is w. The inertial velocity of the center of mass is
zero.

Better to say that we make our measurements in the
(non-rotating) frame of the original centre of mass

Because there are no applied forces or moments, the angular momentum of B is
a constant.

Correct.

Now, suppose my rigid body is instantaneously cut in two parts at time t = 1
sec, resulting in bodies B1 and B2.

1) Does conservation of angular momentum imply that the angular velocity of
B1 and B2 (about their respective mass centers) be equal to w at t = 1 sec?

No, only that angular momentum about the original centre of mass
(or any other inertial point) remains the same. However, I believe
that, if the cut were made in such a way as to not to generate a
lateral force, then the two parts would continue to rotate with
angular velocity w, but conservation of angular momentum does not
require this. It would be possible to make the cut in such a way that
this was not the case, without any external forces acting.

2) In general, will the mass centers of the two bodies, B1 and B2, separate
over time?

Yes, if the angular momentum is not zero.

Why?

All the constituent parts of a rigid body would follow their
own inertial paths (straight lines at constant velocity) if it
were not for the internal forces within the body.

When the cut is made, the force that held the two parts
together and made them act as a single rigid body is
removed. The two parts are now free to move
inertially, in other words the paths of their centres of
mass will be straight lines, whereas they were constrained
to follow circular paths.

3) Will the angular velocity of B1 and B2 remain equal to w if no external
forces or moments are applied to either body?

Yes, if they were when the cut was made.

The angular velocities of B1 and B2 will remain at
their values at the time the cut was made.

Martin Hogbin

"Martin Hogbin" wrote in message ...

....

The angular velocities of B1 and B2 will remain at
their values at the time the cut was made.

Quibble: I believe you meant to write "angular momenta".

The angular velocity, relative to some fixed point or axis, of a mass
point moving in a straight line starts at zero at infinity, reaches a
maximum at the point of closest approach, and falls again to zero as
the point recedes to infinity. The angular momentum of the mass point
remains constant throughout.

This is yet another example of the skater increasing her angular
velocity by pulling in her arms at constant angular momentum -- though
in this case the "pulling in" is purely passive kinematics.

I find that when one has a little auto-didaction in one thread the
same point comes up again and again in other threads passing in the
night.