120 rpm equals approximately 12.5664 radians per second
Converting 120 rpm to radians involves understanding that rpm stands for revolutions per minute, while radians measure angles. Since one revolution equals 2π radians, multiplying by this factor and adjusting for time gives the radian value per second.
Introduction
When converting 120 rpm into radians, the goal is to find out how many radians are swept per second. Knowing that 1 revolution is 2π radians, and 1 minute contains 60 seconds, the conversion involves multiplying by these factors to get 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. This works because each revolution has 2π radians, and dividing by 60 converts minutes into seconds. For example, with 120 rpm: (120 * 2π) / 60 = 12.5664 rad/sec.
Conversion Example
- Convert 60 rpm to rad/sec:
- Multiply 60 by 2π: 60 * 6.2832 = 376.992
- Divide by 60: 376.992 / 60 = 6.2832 rad/sec
- Result: 6.2832 rad/sec
- Convert 90 rpm to rad/sec:
- 90 * 6.2832 = 565.488
- 565.488 / 60 = 9.4248 rad/sec
- Result: 9.4248 rad/sec
- Convert 150 rpm to rad/sec:
- 150 * 6.2832 = 942.48
- 942.48 / 60 = 15.708 rad/sec
- Result: 15.708 rad/sec
Conversion Chart
| rpm | rad/sec |
|---|---|
| 95.0 | 9.9477 |
| 100.0 | 10.472 |
| 105.0 | 10.996 |
| 110.0 | 11.521 |
| 115.0 | 12.045 |
| 120.0 | 12.5664 |
| 125.0 | 13.090 |
| 130.0 | 13.615 |
| 135.0 | 14.139 |
| 140.0 | 14.664 |
| 145.0 | 15.188 |
The table shows how different rpm values convert into radians per second. To read it, find your rpm value in the first column and see its equivalent rad/sec in the second. You can use this for quick reference or comparison.
Related Conversion Questions
- How many radians per second is 120 rpm?
- What is the rad/sec equivalent of 120 revolutions per minute?
- How do I convert 120 rpm to angular velocity in radians?
- What is the radian measure of a 120 rpm rotation per second?
- Convert 120 rpm into radians per second, how do I do that?
- Is 12.5664 radians per second equal to 120 rpm?
- How to calculate radians per second from 120 rpm?
Conversion Definitions
rpm
Revolutions per minute (rpm) indicates how many complete turns or rotations an object makes in one minute. It measures rotational speed, used in engines, machinery, and spinning objects, giving a sense of how fast they rotate over time.
rad
Rad, short for radians, is a measurement of an angle based on the radius of a circle. One radian is the angle where the arc length equals the radius, and there are 2π radians in a full circle, used in mathematical and engineering contexts to describe rotational quantities.
Conversion FAQs
How long does it take for an object rotating at 120 rpm to complete one radian?
At 120 rpm, it completes 120 revolutions in 60 seconds, so one revolution takes 0.5 seconds. Since one revolution has 2π radians, it takes 0.5 / (2π) seconds to cover 1 radian, approximately 0.0796 seconds.
Can I convert rpm to radians per second without a calculator?
Yes, by remembering the formula: radians/sec = rpm * 2π / 60. Basic knowledge of π as approximately 3.1416 helps in doing quick mental estimations, but for precise results, a calculator is recommended.
What is the difference between rpm and rad/sec in terms of measurement?
RPM measures the number of complete rotations per minute, while radians per second measure angular displacement per second, providing a rate of rotation in a different unit system, often used in physics and engineering to analyze rotational dynamics.
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