Elara BennettThe conversion of 45 rpm to radians per second results in approximately 4.7124 rad/sec.
This conversion is based on the fact that revolutions per minute (rpm) can be changed into radians per second (rad/sec) by multiplying by a factor that accounts for the number of radians in a revolution and the seconds in a minute. Since one revolution equals 2π radians, and there are 60 seconds in a minute, the formula involves these constants to get the equivalent angular velocity.
Conversion Result
45 rpm equals about 4.7124 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 equals 2π radians, and there are 60 seconds in one minute. By multiplying rpm by this factor, you get the angular velocity in radians per second.
For example, if you have 45 rpm: 45 * (2π / 60) = 45 * (6.2832 / 60) = 45 * 0.10472 ≈ 4.7124 rad/sec. This step-by-step calculation shows how the constants convert revolutions per minute into radians per second.
Conversion Example
- Convert 60 rpm:
- Multiply 60 by 2π: 60 * 6.2832 = 376.99.
- Divide by 60: 376.99 / 60 = 6.2832 rad/sec.
- Result: 60 rpm is roughly 6.2832 rad/sec.
- Convert 30 rpm:
- Multiply 30 by 2π: 30 * 6.2832 = 188.50.
- Divide by 60: 188.50 / 60 = 3.1416 rad/sec.
- Result: 30 rpm equals about 3.1416 rad/sec.
- Convert 90 rpm:
- Multiply 90 by 2π: 90 * 6.2832 = 565.49.
- Divide by 60: 565.49 / 60 = 9.4248 rad/sec.
- Result: 90 rpm is approximately 9.4248 rad/sec.
Conversion Chart
This chart shows how different rpm values convert into radians per second, helping you quickly find the equivalent for any given number.
| RPM | Radians/sec |
|---|---|
| 20.0 | 2.0944 |
| 25.0 | 2.6179 |
| 30.0 | 3.1416 |
| 35.0 | 3.6652 |
| 40.0 | 4.1888 |
| 45.0 | 4.7124 |
| 50.0 | 5.2360 |
| 55.0 | 5.7596 |
| 60.0 | 6.2832 |
| 65.0 | 6.8068 |
| 70.0 | 7.3304 |
Use this chart to quickly see the rad/sec equivalent for any rpm value by locating the rpm on the left and reading across to the rad/sec value.
Related Conversion Questions
- How many radians per second is 45 rpm?
- What is the rad/sec equivalent of 45 rpm?
- How do I convert 45 rpm into angular radians?
- What formula converts rpm to radians per second for 45 rpm?
- Can you show me the steps to turn 45 rpm into radians?
- What is 45 revolutions per minute in radians per second?
- How many radians does a 45 rpm motor rotate per second?
Conversion Definitions
rpm stands for revolutions per minute, measuring how many full turns an object makes in a minute. Rad is short for radians, the standard unit for measuring angles, with one full revolution equal to 2π radians, used for precise angular measurements.
Conversion FAQs
How accurate is the conversion from rpm to rad/sec?
The conversion is precise as it relies on fundamental constants (2π and 60 seconds). Minor rounding differences may occur when displaying the result to a limited number of decimal places, but the mathematical conversion remains accurate.
Why do we multiply rpm by 2π/60 to get radians per second?
This multiplication accounts for the total radians in one revolution (2π) and converts minutes into seconds by dividing by 60. It effectively translates revolutions per minute into the angular velocity in radians per second.
Can I use this conversion for other units like degrees per second?
No, degrees per second measure angles in degrees, whereas radians are the standard in many calculations involving rotations. To convert rpm to degrees per second, multiply by 360/60, which equals 6 degrees/sec, but for radians, use 2π/60.
