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Name: Fred
Status: educator
Age: 50s
Location: N/A
Country: N/A
Date: 1999 


Question:
I heard that one of the first satellites we launched spun out of control after the radio antennae were deployed. The reason given was that the spin axis of a body will change if the mass is redistributed. In two dimensions, if a skater pulls in her arms she will spin faster because angular momentum is conserved. In three dimensions will something different happen?


Replies:
No. I think the analogy that fits the satellite is simpler: if the skater thinks she's going to pull in both arms but somehow only one comes in, she'll probably fall over.

Is this related to the fact that if you hold a hammer near the end of the handle and give it a toss upward while causing it to spin on an axis perpendicular to the long dimension of the handle, the hammer will begin to spin with an axis parallel to the long dimension of the handle?

Rotations don't mix unless there is some external force.

Tim Mooney


You've got a couple of different issues here, which are related, but not identical. When a skater pulls her arms in, she's changing her "moment of inertia," not her rotational axis. Now, if she pulls just one arm in, she'll change her rotation axis. Unless the axis of a rotating object is fixed, say, by an axle, the axis of any rotation will be its center of mass. This is the case no matter how many dimensions you happen to be living in. The same is true for the conservation of momentum and angular momentum.

As far as the rotation of your tossed hammer is concerned, the moment of inertia about the long axis of the handle is less than about an axis perpendicular to the handle. Thus, a smaller amount of angular momentum will be manifested as a greater angular velocity. When you toss the hammer, even though you are trying to apply torque only about the perpendicular axis, so that the hammer will flip end-over-end, you also will give it some torque about the long axis. It's the same as throwing a ball; although you try to throw it in one direction, you'll miss just a little (or in the case of a klutz like me, a lot), and give it some force in a sideways direction. Since the hammer has angular momentum about both axes, it will spin about both axes.

Richard E. Barrans Jr.
CHM/200/M019
Argonne National Laboratory



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