The result of converting 32 rpm to radians is approximately 3.351 rad.
To convert revolutions per minute (rpm) into radians, you multiply the rpm value by 2π (since one revolution equals 2π radians) and then divide by 60 (seconds in a minute). For 32 rpm, the calculation is (32 × 2π) / 60, which gives about 3.351 radians. This process transforms the rotational speed into an angular measure in radians per second.
Conversion Calculation
Converting rpm to radians involves understanding that each revolution corresponds to 2π radians. Since rpm measures revolutions per minute, to get radians per second, multiply the rpm by 2π and then divide by 60. The formula is: radians/sec = rpm × 2π / 60. For example, 32 rpm: (32 × 2π) / 60 ≈ (32 × 6.2832) / 60 ≈ 201.061 / 60 ≈ 3.351 rad/sec.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to radians is radians = rpm × 2π / 60. This works because each revolution is 2π radians, and since rpm measures revolutions per minute, dividing by 60 converts it into revolutions per second. Multiplying rpm by 2π gives radians per minute, dividing by 60 gives radians per second, which is the angular velocity.
For example, if rpm is 60, then radians = 60 × 2π / 60 = 2π radians per second, which equals approximately 6.2832 rad/sec. This step-by-step calculation ensures you accurately find the angular measure per second from rpm.
Conversion Example
- Convert 45 rpm to radians:
- Multiply 45 by 2π: 45 × 6.2832 = 282.744
- Divide the result by 60: 282.744 / 60 ≈ 4.7124 rad/sec
- Result: Approximately 4.7124 radians per second
- Convert 10 rpm to radians:
- 10 × 2π = 62.832
- 62.832 / 60 ≈ 1.0472 rad/sec
- Result: Approximately 1.0472 radians per second
- Convert 75 rpm to radians:
- 75 × 2π = 471.238
- 471.238 / 60 ≈ 7.8539 rad/sec
- Result: Approximately 7.8539 radians per second
Conversion Chart
This table shows rpm values from 7.0 to 57.0 and their corresponding radians per second. Use this chart to quickly find the radian measure without recalculating each time.
| rpm | radians/sec |
|---|---|
| 7.0 | 0.7330 |
| 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 | 5.9629 |
Read the table by matching the rpm value to find the corresponding radians/sec. Use it when you need quick conversions for these specific rpm values.
Related Conversion Questions
- How many radians per second is 32 rpm?
- What is the radian equivalent of 32 rpm in angular velocity?
- How do I convert 32 rpm to radians per second manually?
- Is there an easy way to convert rpm to radians without calculator?
- What is the formula to switch from rpm to radians in rotational motion?
- How many radians are in 32 rpm of a spinning wheel?
- Can I convert rpm to radians per second using a smartphone app?
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 specify how fast something spins around its axis.
rad
Radian (rad) is a unit of angular measure representing the angle created when the arc length equals the radius. It simplifies calculations in geometry, physics, and engineering by providing a natural measure for angles.
Conversion FAQs
How do I convert 32 rpm to radians per second?
Multiply 32 by 2π to get radians per minute, then divide by 60 to get radians per second. This process accounts for the full rotation in radians and converts the per-minute measure into per-second angular speed.
Why do I divide by 60 in the conversion from rpm to radians?
Because rpm measures revolutions per minute, dividing by 60 converts it into revolutions per second, necessary for calculating radians per second since there are 2π radians in each revolution.
Can I use an online calculator for converting rpm to radians?
Yes, many online tools perform this conversion automatically by applying the formula radians = rpm × 2π / 60, saving time and reducing manual calculation errors.