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200 rpm equals approximately 20.94395 radians per second

Converting 200 rpm to radians involves multiplying the revolutions per minute by a factor to change revolutions to radians and minutes to seconds. The result shows how many radians are swept in one second at 200 rpm.

Introduction

Revolutions per minute (rpm) measures how many times an object spins around its axis in one minute. Radians per second (rad/sec) is a measurement of angular velocity in the SI system, indicating the angle in radians that an object rotates through each second.

Conversion Tool

Conversion Formula

The formula to convert rpm to rad/sec is: angular velocity in rad/sec = rpm * (2π / 60). This works because one revolution equals 2π radians, and there are 60 seconds in a minute. Multiplying rpm by this factor transforms revolutions per minute into radians per second.

For example, if you have 200 rpm, then: 200 * (2π / 60) = 200 * 0.10472 ≈ 20.94395 rad/sec. This step-by-step process shows how the conversion takes place from revolutions to radians and from minutes to seconds.

Conversion Example

• Convert 150 rpm: 150 * (2π / 60) = 150 * 0.10472 ≈ 15.708 rad/sec.
  • Start with rpm: 150
  • Multiply by 2π (≈6.2832)
  • Divide by 60 seconds
  • Calculate: 150 * 6.2832 / 60 ≈ 15.708
• Convert 300 rpm: 300 * (2π / 60) = 300 * 0.10472 ≈ 31.416 rad/sec.
  • Start with 300 rpm
  • Multiply 300 by 6.2832
  • Divide by 60
  • Result: 300 * 6.2832 / 60 ≈ 31.416
• Convert 50 rpm: 50 * (2π / 60) ≈ 8.727 rad/sec.
  • Start with 50 rpm
  • Multiply by 6.2832
  • Divide by 60
  • Calculate: 50 * 6.2832 / 60 ≈ 8.727

Conversion Chart

This chart helps to quickly find the rad/sec equivalent for any rpm between 175 and 225. Read across the row to match the rpm value and see the corresponding radians per second value.

Related Conversion Questions

• How many radians per second is 200 rpm?
• What is the rad/sec equivalent of 200 rpm?
• Convert 200 rpm into radians per second?
• What is the angular velocity in rad/sec for 200 rpm?
• How do I change 200 rpm to radians per second?
• At 200 rpm, what is the rotational speed in radians?
• How many radians does an object rotate per second at 200 rpm?

Conversion Definitions

rpm

Revolutions per minute (rpm) measures how many complete turns an object makes in one minute, indicating the rotational speed. It is used to quantify how fast something spins around its axis in a given amount of time.

rad

Rad, short for radians, is a unit of angular measurement representing the angle created when an arc length equals the radius of a circle. One full revolution equals 2π radians, making it a fundamental measure in angular calculations.

Conversion FAQs

How do I convert 200 rpm to radians per second manually?

Multiply 200 by 2π (about 6.2832), then divide by 60. This converts revolutions per minute to radians per second, giving approximately 20.94395 rad/sec. The formula is rpm * (2π / 60).

Why is the conversion factor 2π/60?

This factor accounts for the full circle in radians (2π) and converts minutes to seconds (divide by 60). It ensures that the revolutions per minute are accurately translated into radians per second, which is the SI angular velocity unit.

Can I use the same formula to convert other rpm values?

Yes, the same formula applies to any rpm value. Just replace the rpm number in the formula rpm * (2π / 60) to find its rad/sec equivalent.

What does the result 20.94395 rad/sec mean physically?

It indicates that at 200 rpm, an object rotates through about 20.94395 radians each second, which signifies its angular velocity or how quickly it spins around its axis in terms of radians per second.