/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 65 Car Engine. Bill's car engine is... [FREE SOLUTION] | 91Ó°ÊÓ

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Car Engine. Bill's car engine is said to run at 1700 RPM's (revolutions per minute) at idle. Through how many degrees does his engine turn each second?

Short Answer

Expert verified
The engine turns approximately 10200 degrees per second.

Step by step solution

01

Understand the Problem

We need to determine how many degrees Bill's car engine turns in one second, given that it runs at 1700 revolutions per minute (RPM).
02

Convert RPM to Revolutions per Second

Since 1 minute is equal to 60 seconds, we need to convert 1700 revolutions per minute to revolutions per second. We divide 1700 by 60: \[ \text{Revolutions per second} = \frac{1700}{60} \approx 28.33 \]
03

Calculate Degrees per Revolution

Each complete revolution of the engine is 360 degrees. This means that each revolution the engine makes turns through 360 degrees.
04

Calculate Degrees per Second

Multiply the number of revolutions per second by the number of degrees in one revolution to find the degrees per second:\[ \text{Degrees per second} = 28.33 \times 360 \approx 10200 \].
05

Summarize the Calculation

Bill's car engine turns approximately 10200 degrees each second while idling.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Revolutions per Minute (RPM)
When you hear the term "RPM," it stands for revolutions per minute. This is a common way to measure the speed of a rotating or spinning object. For instance, car engines, fans, and even wind turbines are often rated by RPMs. Essentially, it's a measure of how many complete turns an object makes in one minute. RPM is a preferred measure because it gives a clear picture of rotational speed over time.
  • Higher RPM means the object is spinning faster.
  • Lower RPM indicates slower spinning.
RPM helps us understand how fast everything that spins is moving, which is crucial for machinery and engines. It can help predict performance and efficiency. Understanding RPM is the first step when converting rotational speeds into other measurements, like degrees per second, which we’ll explore next.
Degree Calculation
A revolution is a full 360-degree rotation. Whenever an object makes one full turn, it has turned through 360 degrees. Therefore, when you calculate degrees from revolutions, you're determining how far something has turned. The transformation from revolutions into degrees is a simple multiplication.
  • Each revolution equals 360 degrees.
  • Multiply the number of revolutions by 360 to find out the degree of motion.
In the exercise, the engine turns approximately 28.33 revolutions each second. To calculate though how many degrees this equates, you perform:\(28.33 \times 360\). This results in about 10,200 degrees each second. Knowing how to convert to degrees helps you understand the angle of rotational movement in practical contexts, like engine speed.
Unit Conversion
Unit conversion is the process of converting a measurement from one unit to another. It’s a critical skill in math and science because it allows you to reshape data in a way that's most useful for the problem you're addressing. In the context of RPM, unit conversion is essential for understanding the speed of rotation over different timescales.
  • To convert RPM to revolutions per second, divide the RPM by 60 (since there are 60 seconds in a minute).
  • In the exercise, 1700 RPM becomes about 28.33 revolutions per second.
Knowing how to carry out unit conversion allows you to understand and work with the measurements in more flexible and meaningful ways, which is incredibly useful across various fields. It bridges the gap between raw data and actionable insights.

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