The problem asks to find the unit rate for 405 rotations in 5 minutes, which means we need to determine how many rotations occur in 1 minute.

To calculate the unit rate, we divide the total number of rotations by the number of minutes: $\text{Unit rate} = \frac{405 \text{ rotations}}{5 \text{ minutes}} = 81 \text{ rotations per minute}.$

Thus, the correct answer is 81 rotations per minute.

Would you like more details or have any questions about the solution?

Here are some related questions you could explore:

1. How do you calculate unit rates in different contexts (e.g., speed, price)?
2. How would the unit rate change if the time period was different (e.g., 10 minutes)?
3. What are some real-life examples where unit rates are useful?
4. How can you apply unit rates to solve problems in everyday life?
5. Can you calculate unit rates when you have decimals involved instead of whole numbers?

Tip: Always remember that to find a unit rate, you divide the total amount by the number of units (in this case, minutes).