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A uniform rod rotates in a gravity-free region with constant angular velocity omega about one of its ends (used as the axis). How does the tensile stress sigma vary with distance x from the axis of rotation? Which graph best represents sigma vs. x?

1. A straight line decreasing from a maximum at x = 0 to zero at x = L
2. A parabola (inverted) decreasing from maximum at x = 0 to zero at x = L
3. A straight line increasing from zero at x = 0 to maximum at x = L
4. A constant (horizontal line)

Correct answer: A parabola (inverted) decreasing from maximum at x = 0 to zero at x = L

Solution

The tensile stress at position x equals the centripetal force required by the portion of the rod beyond x. This gives sigma proportional to (L² - x²), which is an inverted parabola — maximum at x = 0 (the axis) and zero at x = L (the free end).

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