The conversion of 5 rpm to radians per second results in approximately 0.524 rad/sec.
Because 1 rpm equals 2π/60 rad/sec, multiplying 5 rpm by this factor gives the rad/sec value. This straightforward calculation converts revolutions per minute into radians per second by applying the angular measure of a full circle (2π radians) divided by the time in seconds.
Conversion Result
5 rpm is equal to roughly 0.524 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 one revolution equals 2π radians, and there are 60 seconds in a minute, so multiplying rpm by the radians per second factor gives the angular velocity in rad/sec. For example, 5 rpm times (2π/60) equals 0.524 rad/sec, calculated as 5 × (6.2832 / 60) ≈ 0.524.
Conversion Example
- Convert 10 rpm to rad/sec:
- Step 1: Write the formula: 10 × (2π / 60).
- Step 2: Calculate 2π ≈ 6.2832.
- Step 3: Divide 6.2832 by 60: 6.2832 / 60 ≈ 0.1047.
- Step 4: Multiply 10 by 0.1047: 10 × 0.1047 ≈ 1.047 rad/sec.
- Convert 15 rpm to rad/sec:
- Step 1: Formula: 15 × (2π / 60).
- Step 2: 2π ≈ 6.2832.
- Step 3: 6.2832 / 60 ≈ 0.1047.
- Step 4: 15 × 0.1047 ≈ 1.571 rad/sec.
- Convert 20 rpm to rad/sec:
- Step 1: Formula: 20 × (2π / 60).
- Step 2: 2π ≈ 6.2832.
- Step 3: 6.2832 / 60 ≈ 0.1047.
- Step 4: 20 × 0.1047 ≈ 2.094 rad/sec.
Conversion Chart
| rpm | rad/sec |
|---|---|
| -20.0 | -1.0472 |
| -15.0 | -0.7854 |
| -10.0 | -0.5236 |
| -5.0 | -0.2618 |
| 0.0 | 0.0 |
| 5.0 | 0.2618 |
| 10.0 | 0.5236 |
| 15.0 | 0.7854 |
| 20.0 | 1.0472 |
| 25.0 | 1.3089 |
| 30.0 | 1.5708 |
This chart shows rpm values from -20 to 30 and their corresponding rad/sec equivalents. To use, find your rpm value in the first column, then read across to see the rad/sec value. It helps quickly estimate conversions for common speeds.
Related Conversion Questions
- How many radians per second are in 5 rpm?
- What is the rad/sec equivalent of 5 rpm?
- Convert 5 rpm to radians per second for a motor speed?
- How do I change 5 rpm into angular velocity in radians?
- What is the rad/sec value when rpm is 5?
- How to calculate radians per second from 5 revolutions per minute?
- Is 5 rpm equal to approximately 0.524 rad/sec?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many full rotations an object completes in one minute. It is a common way to express rotational speed, especially in engines and motors, indicating how fast something spins.
rad
Rad, short for radians, measures angular distance around a circle. One radian is the angle where the arc length equals the radius. It provides a natural way to quantify rotation, with a full circle being 2π radians.
Conversion FAQs
Why is the factor 2π/60 used in rpm to rad/sec conversion?
This factor arises because each revolution equals 2π radians, and there are 60 seconds in a minute. Multiplying rpm by 2π/60 converts revolutions per minute into radians per second by combining these two measures into a single angular velocity value.
Can I convert rpm to rad/sec manually without a calculator?
Yes, by remembering that 1 rpm equals approximately 0.1047 rad/sec, you can multiply rpm by this number for quick estimates. For precise results, use the formula with 2π/60, which is roughly 0.10472.
How does the conversion change if the rpm value is negative?
Negative rpm indicates reverse rotation; the rad/sec value will also be negative, reflecting direction. The magnitude remains the same, but the sign shows the opposite rotational direction.
What are common uses of rad/sec in engineering?
Rad/sec are used to describe angular velocity in mechanical and electrical engineering, such as motor speeds, rotational dynamics, and oscillations, where precise angular measurements are necessary for design and analysis.