Two rods are rotating about two fixed points in opposite directions. If
they start from their position of coincidence and one rotates at the rate
double that of the other, then find the locus of point of the intersection of
the two rods.
Text Solution
AI Generated Solution
To find the locus of the point of intersection of two rods rotating about fixed points in opposite directions, we can follow these steps:
### Step-by-Step Solution:
1. **Understanding the Setup**:
- We have two rods rotating about fixed points. Let's denote the fixed point for the first rod as \( O \) (at the origin, \( (0, 0) \)) and the fixed point for the second rod as \( A \) (at \( (a, 0) \)).
- The first rod rotates with an angular speed \( \omega \) and the second rod rotates with an angular speed \( 2\omega \).
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