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The conversion of 50 rpm to radians per second equals approximately 5.236 rad/sec.
To convert revolutions per minute (rpm) to radians, we recognize that one revolution equals 2π radians, and there are 60 seconds in a minute. So, multiplying rpm by 2π and dividing by 60 gives the rad/sec value. For example, 50 rpm times 2π, then divided by 60, results in about 5.236 radians per second.
Conversion Result
50 rpm is equivalent to approximately 5.236 radians per second.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to radian per second is: radians/sec = rpm * 2π / 60. It works because one revolution equals 2π radians and there are 60 seconds in a minute. So, multiplying rpm by 2π converts revolutions into radians, then dividing by 60 adjusts to seconds.
For example, with 50 rpm:
- 50 rpm * 2π = 50 * 6.2832 ≈ 314.16 radians per minute
- 314.16 / 60 ≈ 5.236 radians per second
Conversion Example
Convert 75 rpm to rad/sec:
- Multiply 75 by 2π: 75 * 6.2832 ≈ 471.24 radians per minute
- Divide 471.24 by 60: 471.24 / 60 ≈ 7.854 rad/sec
This means 75 rpm equals approximately 7.854 rad/sec.
Conversion Chart
| rpm | rad/sec |
|---|---|
| 25.0 | 2.6180 |
| 30.0 | 3.1416 |
| 35.0 | 3.6652 |
| 40.0 | 4.1888 |
| 45.0 | 4.7124 |
| 50.0 | 5.2360 |
| 55.0 | 5.7596 |
| 60.0 | 6.2832 |
| 65.0 | 6.8068 |
| 70.0 | 7.3304 |
| 75.0 | 7.8540 |
This chart shows rpm values from 25 to 75 and their corresponding rad/sec conversions. Use it to quickly find the rad/sec value for a given rpm, or vice versa.
Related Conversion Questions
- How many radians per second is 50 rpm?
- What is the radian equivalent of 60 rpm?
- How do I convert 75 rpm to radians per second?
- What is the formula to change rpm into rad/sec for any value?
- Can I convert rpm to radians using an online calculator for 50 rpm?
- What is the angular velocity in radians/sec for 100 rpm?
- How does the conversion from rpm to rad/sec work for rotational speed?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns an object makes in one minute. It quantifies rotational speed, with higher rpm indicating faster spinning, and is used in engines, motors, and rotating machinery.
rad
Radian (rad) is a measure of angle based on the radius of a circle, where one radian equals the angle at the center of a circle that subtends an arc length equal to the radius. It provides a natural way to describe angles in mathematics and physics.
Conversion FAQs
How do I convert rpm to radians per second manually?
Multiply the rpm value by 2π to get radians per minute, then divide by 60 to convert to radians per second. For example, 50 rpm times 2π gives 314.16 radians per minute. Dividing by 60 results in about 5.236 rad/sec.
Why is the division by 60 necessary in the conversion?
The division by 60 accounts for the number of seconds in a minute, transforming the angular velocity from per minute to per second, aligning with SI units and standard measurement practices.
Can I use a calculator to instantly convert rpm to rad/sec?
Yes, many online calculators or scientific calculators can perform this conversion. You simply input the rpm value and multiply by 2π, then divide by 60 to get rad/sec.
What happens if I convert 0 rpm to radians?
Zero rpm indicates no rotation, so the rad/sec value is also zero, meaning there is no angular velocity or movement occurring.
