32 rpm is approximately 3.351 rad per second
Converting 32 rpm to radians involves understanding that rpm measures revolutions per minute, and radians per second expresses angular velocity in terms of radians over time. When we convert, 32 rpm results in about 3.351 radians per second, which is useful in physics and engineering applications.
Understanding the Conversion from rpm to rad
The conversion formula relies on knowing that one revolution equals 2π radians, and there are 60 seconds in a minute. To change rpm to rad/sec, we multiply revolutions per minute by 2π to get radians per minute, then divide by 60 to convert to radians per second. For example, with 32 rpm: (32 × 2π) / 60 ≈ 3.351 rad/sec.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to rad/sec is (rpm × 2π) / 60. It works because each revolution contains 2π radians, and dividing by 60 seconds converts revolutions per minute into radians per second. For example, if rpm is 50, then rad/sec = (50 × 2π) / 60 ≈ 5.236 rad/sec.
Conversion Example
- Convert 45 rpm to rad/sec:
- Multiply 45 by 2π: 45 × 6.2832 ≈ 282.743
- Divide by 60: 282.743 / 60 ≈ 4.712 rad/sec
- Convert 10 rpm to rad/sec:
- 10 × 2π ≈ 62.832
- Divide by 60: 62.832 / 60 ≈ 1.047 rad/sec
- Convert 100 rpm to rad/sec:
- 100 × 2π ≈ 628.319
- Divide by 60: 628.319 / 60 ≈ 10.472 rad/sec
Conversion Chart
This chart displays rpm values from 7.0 to 57.0 and their corresponding rad/sec conversions so you can quickly find approximate values.
| RPM | Radians/sec |
|---|---|
| 7.0 | 0.7330 |
| 8.0 | 0.8378 |
| 9.0 | 0.9426 |
| 10.0 | 1.0472 |
| 15.0 | 1.5708 |
| 20.0 | 2.0944 |
| 25.0 | 2.6180 |
| 30.0 | 3.1416 |
| 35.0 | 3.6652 |
| 40.0 | 4.1888 |
| 45.0 | 4.7124 |
| 50.0 | 5.2360 |
| 55.0 | 5.7596 |
| 57.0 | 5.9580 |
Read the table by locating your rpm value in the first column and then look across to find the corresponding rad/sec in the second column.
Related Conversion Questions
- How many radians per second is 32 rpm equivalent to in a rotating motor?
- What is the rad/sec value for 32 rpm in a physics experiment?
- Can I convert 32 revolutions per minute to radians per second easily?
- What is the angular velocity in radians/sec if a wheel spins at 32 rpm?
- How do I calculate radians per second from rpm for a given value like 32?
- What is the conversion factor from rpm to radians/sec for 32 rpm?
- How to convert 32 rpm into angular displacement in radians per second?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns or rotations an object makes in one minute, used in machinery and engines to indicate rotational speed.
rad
Rad or radians are a unit of angular measurement, where one radian equals the angle formed when the arc length equals the radius of a circle. It measures how far an object has rotated around a circle.
Conversion FAQs
Why is it necessary to convert rpm to rad/sec for some calculations?
Converting rpm to rad/sec allows for compatibility with formulas in physics and engineering, like calculating torque or angular acceleration, which use radians per second as standard units for angular velocity.
How do I convert rpm to rad/sec manually without a calculator?
Multiply the rpm value by 2π, then divide by 60. For example, for 20 rpm: (20 × 6.2832) / 60 ≈ 2.094 rad/sec, which gives the angular velocity in radians per second.
What is the significance of 2π in the conversion formula?
2π radians correspond to one full revolution, so multiplying rpm by 2π converts revolutions into radians, the standard measure for angular displacement.
Can I use this conversion to determine the angular velocity in other units?
Yes, once you find radians per second, you can convert to degrees per second by multiplying by 180/π or to revolutions per second by dividing rpm by 60.