Problem 31 - Algebra 2 and Trigonometry

Question

The blades of a windmill make one complete rotation per second. How many rotations do they make in one minute?

Step-by-Step Solution

Answer

The windmill makes 60 rotations in one minute.

Step 1: Understanding the Problem

The problem is asking how many complete rotations the windmill blades make in one minute, given that they make one complete rotation per second.

Step 2: Identifying Key Information

We know there is 1 rotation per second. We also know there are 60 seconds in one minute.

Step 3: Setting Up the Calculation

To find the total rotations in one minute, we need to multiply the number of rotations per second by the number of seconds in a minute. This can be expressed as: \(1 \text{ rotation/second} \times 60 \text{ seconds} \).

Step 4: Performing the Calculation

Calculate the total number of rotations: \(1 \times 60 = 60\) rotations.

Step 5: Concluding the Solution

The blades of the windmill make 60 rotations in one minute.

Key Concepts

Understanding Rotational Speed

Rotational speed is essentially how fast an object spins or rotates. In our exercise, the windmill blades make one full rotation every second. This means their rotational speed is 1 rotation per second.

To visualize this, imagine standing in front of the windmill. If you counted the blades each second, you'd say "one rotation" at the end of each second as the blades complete a full circle. When we talk about rotational speed, we consider:

• The number of rotations completed within a certain time frame.
• Units like rotations per second (rps) or rotations per minute (rpm).

Understanding this concept helps us analyze and solve problems involving rotating objects, such as wheels, fans, or in this case, a windmill.

The Basics of Time Conversion

Time conversion is a useful skill when you need to express the same event or rate in different units of time. In the windmill exercise, we needed to convert rotations per second to rotations per minute.

Think of it like this: We know there are 60 seconds in one minute. So, to find out how many rotations occur in one minute, you multiply the rotations in one second by the number of seconds in a minute. In a typical scenario:

• If it's 1 rotation per second, and 60 seconds in a minute, the calculation is simple: 1 rotation/second × 60 seconds = 60 rotations per minute.

This approach is useful anytime you're converting time-related quantities from smaller units to larger units or vice versa.

Solving with Basic Arithmetic Operations

Basic arithmetic operations are fundamental to solving many everyday math problems, including those involving rotational speed and time conversion. In our windmill problem, multiplication was the key operation used.

When we calculated the windmill's rotations, we performed a multiplication operation:

• We multiplied the rotational speed (1 rotation per second) by the conversion factor (60 seconds per minute): 1 × 60 = 60 rotations.

Understanding how to properly apply multiplication can simplify many tasks, like determining rates, converting units, or even solving more complex equations.

By mastering these basic operations, we lay the groundwork for tackling more advanced math problems confidently.