120 rpm equals approximately 12.5664 radians per second
Converting 120 rpm to radians per second results in about 12.5664 rad/sec. This is because 1 rpm equals 2π/60 rad/sec, so multiply 120 by that factor to get the value in radians.
Understanding the Conversion Process
To convert revolutions per minute to radians per second, you multiply the rpm value by 2π (which is the radians in one revolution) and then divide by 60 seconds (the minutes). This converts the rotational speed from revolutions per minute to radians per second.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to rad/sec is: radians per second = rpm * 2π / 60. It works because one revolution is 2π radians, and dividing by 60 seconds converts minutes to seconds. For example, for 120 rpm, multiply 120 by 2π then divide by 60.
Conversion Example
- Suppose you want to convert 90 rpm:
- Multiply 90 by 2π: 90 * 6.2832 ≈ 565.488
- Then divide by 60: 565.488 / 60 ≈ 9.4248 rad/sec
- So, 90 rpm is approximately 9.4248 radians per second.
- For 45 rpm:
- 45 * 2π ≈ 282.743
- Divide by 60: 282.743 / 60 ≈ 4.7124 rad/sec
- Thus, 45 rpm equals about 4.7124 rad/sec.
- And for 150 rpm:
- 150 * 2π ≈ 942.4778
- Divide by 60: 942.4778 / 60 ≈ 15.708 rad/sec
- Therefore, 150 rpm corresponds to roughly 15.708 rad/sec.
Conversion Chart
| rpm | rad/sec |
|---|---|
| 95.0 | 9.9587 |
| 100.0 | 10.4719 |
| 105.0 | 11.0053 |
| 110.0 | 11.5397 |
| 115.0 | 12.0741 |
| 120.0 | 12.5664 |
| 125.0 | 13.1008 |
| 130.0 | 13.6352 |
| 135.0 | 14.1696 |
| 140.0 | 14.704 |
| 145.0 | 15.2384 |
This chart helps you see how different rpm values convert to radians per second. Find your rpm value in the first column, then read across to see the equivalent radians per second.
Related Conversion Questions
- How many radians per second is 120 rpm?
- What is the rad/sec equivalent of 120 rpm?
- Convert 120 rpm to radians per second manually?
- Why does 120 rpm equal approximately 12.5664 rad/sec?
- How do I convert rpm to radians in a calculator for 120 rpm?
- What is the formula used for converting 120 rpm to radians?
- Is 120 rpm a high or low rotational speed in radians?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many full turns an object makes in one minute, indicating rotational speed. It is used in engines, motors, and machinery to describe how fast something spins, with higher rpm meaning faster rotation.
rad
Rad is short for radians, a unit measuring angles based on the radius of a circle. One radian equals the angle where the arc length equals the radius, and there are 2π radians in a full circle. It’s used in mathematics and physics to quantify angular measures precisely.
Conversion FAQs
How accurate is the conversion from rpm to rad/sec?
The conversion formula used provides precise results because it directly applies the mathematical relationship between revolutions, radians, and seconds. Minor rounding differences may occur when results are rounded to four decimal places.
Can I convert any rpm value to radians per second using this method?
Yes, the method applies universally because it’s based on fundamental mathematical principles. For any rpm, multiply by 2π and divide by 60, regardless of the value.
Why do I need to divide by 60 in the formula?
Dividing by 60 converts minutes to seconds because rpm is per minute, but radians per second require seconds. This ensures the units are consistent and the rate reflects radians traveled per second.
What is the significance of 2π in the conversion?
2π represents the radians in one full revolution of a circle. It’s a constant factor in the conversion because it relates the linear measure (revolutions) to the angular measure (radians).