Show that if a rod held at angle `theta` to the horizontal and released, its lower end will not slip if the friction coefficient between rod and ground is greater than `(3sinthetacostheta)/(1+3sin^(2)theta)`

Explanation

To solve the problem, we need to analyze the forces and torques acting on the rod when it is released from an angle θ with respect to the horizontal. We will derive the condition under which the lower end of the rod does not slip.

### Step-by-Step Solution:

1. **Identify Forces Acting on the Rod**:
- The weight of the rod (mg) acts downward at its center of mass, which is located at a distance of \( \frac{L}{2} \) from the lower end.
- The normal force (N) acts upward at the point of contact with the ground.
- The frictional force (f) acts horizontally at the point of contact, opposing the motion.
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