The conversion of 5 rpm to radians per second results in approximately 0.5236 rad/sec.
This is because rpm (revolutions per minute) can be converted to radians per second by multiplying the rpm value by 2π (since one revolution equals 2π radians) and then dividing by 60 (seconds in a minute). So, 5 rpm equals (5 × 2π) / 60 rad/sec.
Conversion Result
The value of 5 rpm equals about 0.5236 radians per second, which indicates how many radians the object rotates each second at this speed.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to rad/sec is: radians per second = (rpm × 2π) / 60. This works because a full rotation is 2π radians, and there are 60 seconds in a minute, so dividing by 60 converts revolutions per minute into revolutions per second, then into radians.
For example, for 5 rpm: (5 × 2π) / 60 = (5 × 6.2832) / 60 = 31.416 / 60 = 0.5236 rad/sec.
Conversion Example
- Convert 10 rpm:
- Multiply 10 by 2π: 10 × 6.2832 = 62.832
- Divide by 60: 62.832 / 60 = 1.0472 rad/sec
- Convert 15 rpm:
- 15 × 6.2832 = 94.248
- 94.248 / 60 = 1.5708 rad/sec
- Convert 20 rpm:
- 20 × 6.2832 = 125.664
- 125.664 / 60 = 2.0944 rad/sec
- Convert 25 rpm:
- 25 × 6.2832 = 157.08
- 157.08 / 60 = 2.6180 rad/sec
Conversion Chart
| rpm | radians/sec |
|---|---|
| -20.0 | -2.0944 |
| -15.0 | -1.5708 |
| -10.0 | -1.0472 |
| -5.0 | -0.5236 |
| 0.0 | 0.0 |
| 5.0 | 0.5236 |
| 10.0 | 1.0472 |
| 15.0 | 1.5708 |
| 20.0 | 2.0944 |
| 25.0 | 2.6180 |
| 30.0 | 3.1416 |
This chart helps you quickly find the rad/sec equivalent for any rpm value listed, simply by matching the rpm to its rad/sec value.
Related Conversion Questions
- What is the rad/sec value for 5 rpm?
- How do I convert 5 rpm to radians per second manually?
- What is the angular velocity in radians/sec for 5 rpm?
- Can I convert 5 rpm to radians per second using an online calculator?
- What is the formula to change rpm to radians/sec for 5 rpm?
- How many radians does an object rotate each second at 5 rpm?
- Is 0.5236 rad/sec the correct conversion for 5 rpm?
Conversion Definitions
rpm, revolutions per minute, measures how many complete turns an object makes in a minute, indicating rotational speed. rad, radians, is a unit of angular measure representing the angle of rotation in a circle, where 2π radians equal one full revolution.
Conversion FAQs
How accurate is the conversion from rpm to rad/sec?
The conversion is precise as long as the mathematical constants and calculations are correctly used, specifically multiplying by 2π and dividing by 60. Minor rounding errors can occur when using approximate decimal values for π.
Can I use the same formula for converting other units of rotational speed?
No, different units like degrees per second or revolutions per second require their own conversion factors. The rpm to rad/sec formula specifically relies on the relationship between revolutions, radians, and seconds.
Why is dividing by 60 necessary in the conversion?
Dividing by 60 converts minutes into seconds because rpm measures revolutions per minute, but radians per second requires the rate per second. This step ensures the units are correctly aligned for the rad/sec measurement.
What is the significance of 2π in the conversion?
2π radians equals one full revolution. Multiplying rpm by 2π converts revolutions into radians, which are a more fundamental measure of angles, making the conversion accurate for angular velocity calculations.