120 rpm equals approximately 12.5664 radians per second.
To convert revolutions per minute (rpm) to radians per second (rad/sec), multiply the rpm value by 2π and then divide by 60. This process converts the number of full rotations per minute into the angle in radians traveled each second.
Conversion Result
120 rpm is approximately 12.5664 radians per second.
This calculation is done by taking the revolutions per minute, multiplying by 2π to get radians per minute, then dividing by 60 to get radians per second, which is the standard SI unit for angular velocity.
Conversion Tool
Result in rad:
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 2π converts revolutions to radians per minute, then dividing by 60 gives radians per second. For example, for 120 rpm: 120 * 2π / 60 = (120/60) * 2π = 2 * 3.1416 ≈ 6.2832 rad/sec.
Conversion Example
- Convert 60 rpm to rad/sec:
- Step 1: Multiply 60 by 2π: 60 * 6.2832 ≈ 376.99 radians per minute
- Step 2: Divide by 60: 376.99 / 60 ≈ 6.2832 rad/sec
- Convert 180 rpm to rad/sec:
- Step 1: 180 * 6.2832 ≈ 1130.97 radians per minute
- Step 2: 1130.97 / 60 ≈ 18.8495 rad/sec
- Convert 90 rpm to rad/sec:
- Step 1: 90 * 6.2832 ≈ 565.49 radians per minute
- Step 2: 565.49 / 60 ≈ 9.4248 rad/sec
- Convert 30 rpm to rad/sec:
- Step 1: 30 * 6.2832 ≈ 188.50 radians per minute
- Step 2: 188.50 / 60 ≈ 3.1416 rad/sec
- Convert 150 rpm to rad/sec:
- Step 1: 150 * 6.2832 ≈ 942.48 radians per minute
- Step 2: 942.48 / 60 ≈ 15.708 rad/sec
Conversion Chart
| rpm | Radians per second (rad/sec) |
|---|---|
| 95.0 | 9.9583 |
| 100.0 | 10.4720 |
| 105.0 | 10.9857 |
| 110.0 | 11.4994 |
| 115.0 | 12.0131 |
| 120.0 | 12.5664 |
| 125.0 | 13.0801 |
| 130.0 | 13.5938 |
| 135.0 | 14.1075 |
| 140.0 | 14.6212 |
| 145.0 | 15.1349 |
This chart helps you find the rad/sec value for any rpm between 95 and 145 by matching the rpm to the corresponding rad/sec.
Related Conversion Questions
- How many radians per second is 120 rpm?
- What is the rad/sec equivalent of 120 rpm?
- Convert 120 revolutions per minute to radians per second?
- How do I change 120 rpm into radians per second manually?
- What is the angular velocity in radians for 120 rpm?
- Is 120 rpm equal to approximately 12.57 rad/sec?
- How can I convert rpm to radians for a motor spinning at 120 rpm?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many full turns an object makes in a minute, often used to describe rotational speed of engines, wheels, or turbines, indicating how quickly they spin relative to time in minutes.
rad
Rad, short for radians, is a unit of angular measurement that describes the size of an angle based on the radius of a circle, with one radian being the angle where the arc length equals the radius, used in mathematics and physics for precise angle calculations.
Conversion FAQs
What does 120 rpm equate to in radians per second?
120 rpm equals about 12.5664 radians per second because multiplying 120 rpm by 2π and dividing by 60 gives the radians traveled each second, representing the angular velocity.
How can I convert rpm to radians manually?
To convert rpm to radians per second manually, multiply the rpm value by 2π and then divide by 60. This converts revolutions per minute into radians per second, which measures how fast something spins in radians each second.
Why is the factor 2π used in conversions?
The factor 2π is used because one full revolution equals 2π radians. This relationship allows us to convert rotational counts into angular measurements, making calculations consistent with the circle’s geometry.
Is there an easy way to estimate rad/sec from rpm without a calculator?
You can estimate by noting that 60 rpm is approximately 6.2832 rad/sec, so for other rpm values, you can scale proportionally, but for exact results, the formula involving 2π divided by 60 is needed.