Math Problem Statement

Under normal conditions, how many revolutions does the rotor spin per minute?

Solution

To find how many revolutions the rotor spins per minute under normal conditions, we can calculate the constant rate based on the information in the table.

The time and revolutions in the table suggest that the number of revolutions is increasing at a constant rate, meaning we can determine the revolutions per minute by calculating the difference in revolutions over a given time interval.

From the table:

  • In 1 minute, the rotor completes 1,750 revolutions.
  • In 3 minutes, the rotor completes 5,250 revolutions.

To calculate the rate in revolutions per minute:

  1. Subtract the revolutions in 1 minute from those in 3 minutes: 5,2501,750=3,500 revolutions over 2 minutes.5,250 - 1,750 = 3,500 \text{ revolutions over 2 minutes}.

  2. Divide this by the 2 minutes: 3,5002=1,750 revolutions per minute.\frac{3,500}{2} = 1,750 \text{ revolutions per minute}.

Thus, the rotor spins at 1,750 revolutions per minute. Therefore, the correct answer is C) 1,750 revolutions per minute.

Do you want any further details or have any questions?

Here are 5 related questions you could explore:

  1. How do you calculate the average speed or rate of any machine or system over time?
  2. What is the difference between linear and non-linear rates of change?
  3. How would you solve a similar problem if the rate of revolutions was not constant?
  4. How can you calculate revolutions per second based on revolutions per minute?
  5. How can this concept be applied to other rotating objects, like a car’s engine or fan blades?

Tip: Always ensure the time intervals used in rate calculations match the unit you need (e.g., per minute, per second).

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Math Problem Analysis

Mathematical Concepts

Rate of Change
Constant Rate
Proportionality

Formulas

Revolutions per minute = Total Revolutions / Total Time

Theorems

Linear Proportionality

Suitable Grade Level

Grades 6-8