- #1
bryanso
- 28
- 7
- Homework Statement
- Feynman Lectures Volume 1 Chapter 19 has the following discussion. I understand the mathematic proof, but I don't understand his thinking.
- Relevant Equations
- Not a question about equations, but this is a discussion of the Parallel Axis Theorem
https://www.feynmanlectures.caltech.edu/I_19.html
"Suppose we have an object, and we want to find its moment of inertia around some axis. That means we want the inertia needed to carry it by rotation about that axis. Now if we support the object on pivots at the center of mass, so that the object does not turn as it rotates about the axis (because there is no torque on it from inertial effects, and therefore it will not turn when we start moving it), then the forces needed to swing it around are the same as though all the mass were concentrated at the center of mass, and the moment of inertia would be simply ##I_1 = M R^2_{cm}##, where ##R_{cm}## is the distance from the axis to the center of mass..."
I'm really stuck at understanding a pivot supporting the center of mass. I take it to mean fixing the center of mass at a fixed location, not allowing it to move. Then how can it be moved?
Next, he said "so that the object does not turn as it rotates about the axis"... Aren't turn and rotate the same thing? How can something rotate but not turn?
Thanks
"Suppose we have an object, and we want to find its moment of inertia around some axis. That means we want the inertia needed to carry it by rotation about that axis. Now if we support the object on pivots at the center of mass, so that the object does not turn as it rotates about the axis (because there is no torque on it from inertial effects, and therefore it will not turn when we start moving it), then the forces needed to swing it around are the same as though all the mass were concentrated at the center of mass, and the moment of inertia would be simply ##I_1 = M R^2_{cm}##, where ##R_{cm}## is the distance from the axis to the center of mass..."
I'm really stuck at understanding a pivot supporting the center of mass. I take it to mean fixing the center of mass at a fixed location, not allowing it to move. Then how can it be moved?
Next, he said "so that the object does not turn as it rotates about the axis"... Aren't turn and rotate the same thing? How can something rotate but not turn?
Thanks