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Table of Contents
15 rpm equals approximately 1.57 radians per second
When converting 15 revolutions per minute (rpm) to radians, the result is about 1.57 radians. This conversion shows how many radians are in each revolution, scaled by the number of revolutions per minute, and then converted to radians per second for standard measurement.
Introduction
The conversion from rpm to rad involves understanding the relationship between revolutions and radians. Since one revolution equals 2π radians, converting rpm to radians per second involves multiplying the rpm by 2π and then dividing by 60, because there are 60 seconds in a minute.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to radians involves multiplying the rpm value by 2π (since one revolution equals 2π radians) and then dividing by 60 to convert minutes to seconds. Mathematically, it looks like: radians/sec = (rpm * 2π) / 60. For example, 15 rpm: (15 * 2π) / 60 = (15 * 6.2832) / 60 ≈ 1.57 rad/sec.
Conversion Example
- Convert 10 rpm:
- Multiply 10 by 2π: 10 * 6.2832 = 62.832
- Divide by 60: 62.832 / 60 = 1.0488 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 = 2.618 rad/sec
- Convert 5 rpm:
- 5 * 6.2832 = 31.416
- 31.416 / 60 = 0.5236 rad/sec
Conversion Chart
| rpm | Radians per second (rad/sec) |
|---|---|
| -10.0 | -1.0472 |
| -5.0 | -0.5236 |
| 0.0 | 0.0000 |
| 5.0 | 0.5236 |
| 10.0 | 1.0488 |
| 15.0 | 1.57 |
| 20.0 | 2.0944 |
| 25.0 | 2.6180 |
| 30.0 | 3.1416 |
| 35.0 | 3.6652 |
| 40.0 | 4.1888 |
Use this chart to quickly find the rad/sec value for any rpm in the range from -10 to 40 by reading across the table.
Related Conversion Questions
- How many radians are in 15 rpm?
- What is the rad/sec equivalent of 15 rpm?
- How do I convert 15 rpm to angular velocity in radians per second?
- If a motor spins at 15 rpm, what is its speed in radians?
- Can you show me the formula to change 15 rpm to radians per second?
- What is the rad/sec value for 15 revolutions per minute?
- How to calculate radians per second from rpm for 15 rpm?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns an object makes in one minute, indicating rotational speed. It is used in engines, motors, and machinery to describe how fast something spins.
rad
Radians (rad) measure angles based on the radius of a circle, where one radian equals the angle at which the arc length equals the radius. It is a standard unit for angular measurement in mathematics and physics.
Conversion FAQs
Why is the conversion from rpm to radians important?
This conversion is vital because many physics and engineering formulas require angular velocity in radians per second, allowing for consistent calculations in rotational dynamics, energy, and motion analysis.
Can I convert any rpm value to radians per second using the same formula?
Yes, the same formula applies universally: radians/sec = (rpm * 2π) / 60. It works for any rpm value, positive or negative, to find the equivalent angular velocity in radians per second.
What does a rad/sec value tell me about a rotating object?
It indicates how fast the object rotates in terms of angular displacement per second, providing a standard measure to compare rotational speeds regardless of the size of the object or the number of revolutions.
