1200 rpm is approximately 125.66 radians per second
Converting 1200 rpm to radians per second results in about 125.66 rad/s. This is because one revolution per minute equals 0.10472 radians per second, so multiplying 1200 by this factor gives the radian value.
Explanation of the Conversion
The conversion from rpm (revolutions per minute) to radians per second involves understanding that one revolution is 2π radians and there are 60 seconds in a minute. Therefore, to convert rpm to rad/sec, you multiply rpm by 2π and divide by 60, which simplifies to multiplying by π/30. For example, 1200 rpm times π/30 equals 125.66 rad/sec.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to rad/sec is: radians/sec = rpm * (2π / 60). This works because each revolution is 2π radians, and there are 60 seconds in a minute, adjusting the units accordingly. By multiplying rpm by π/30, you get radians per second directly.
For example, if you have 1200 rpm, then: 1200 * (2π / 60) = 1200 * (π / 30) = 1200 / 30 * π = 40 * π = approximately 125.66 rad/sec.
Conversion Example
- Convert 600 rpm:
- Use the formula: 600 * (π / 30)
- Divide 600 by 30: 20
- Multiply by π: 20 * 3.1416 = 62.832 rad/sec
- Convert 900 rpm:
- Use the formula: 900 * (π / 30)
- Divide 900 by 30: 30
- Multiply by π: 30 * 3.1416 = 94.248 rad/sec
- Convert 1500 rpm:
- Use the formula: 1500 * (π / 30)
- Divide 1500 by 30: 50
- Multiply by π: 50 * 3.1416 = 157.08 rad/sec
Conversion Chart
| rpm | radians/sec |
|---|---|
| 1175.0 | 1175.0 * (π / 30) ≈ 122.99 |
| 1176.0 | 1176.0 * (π / 30) ≈ 123.14 |
| 1177.0 | 1177.0 * (π / 30) ≈ 123.28 |
| 1178.0 | 1178.0 * (π / 30) ≈ 123.43 |
| 1179.0 | 1179.0 * (π / 30) ≈ 123.57 |
| 1180.0 | 1180.0 * (π / 30) ≈ 123.71 |
| 1181.0 | 1181.0 * (π / 30) ≈ 123.86 |
| 1182.0 | 1182.0 * (π / 30) ≈ 124.00 |
| 1183.0 | 1183.0 * (π / 30) ≈ 124.15 |
| 1184.0 | 1184.0 * (π / 30) ≈ 124.29 |
| 1185.0 | 1185.0 * (π / 30) ≈ 124.43 |
| 1186.0 | 1186.0 * (π / 30) ≈ 124.58 |
| 1187.0 | 1187.0 * (π / 30) ≈ 124.72 |
| 1188.0 | 1188.0 * (π / 30) ≈ 124.86 |
| 1189.0 | 1189.0 * (π / 30) ≈ 125.01 |
| 1190.0 | 1190.0 * (π / 30) ≈ 125.15 |
| 1191.0 | 1191.0 * (π / 30) ≈ 125.29 |
| 1192.0 | 1192.0 * (π / 30) ≈ 125.43 |
| 1193.0 | 1193.0 * (π / 30) ≈ 125.58 |
| 1194.0 | 1194.0 * (π / 30) ≈ 125.72 |
| 1195.0 | 1195.0 * (π / 30) ≈ 125.86 |
| 1196.0 | 1196.0 * (π / 30) ≈ 126.00 |
| 1197.0 | 1197.0 * (π / 30) ≈ 126.15 |
| 1198.0 | 1198.0 * (π / 30) ≈ 126.29 |
| 1199.0 | 1199.0 * (π / 30) ≈ 126.43 |
| 1200.0 | 1200.0 * (π / 30) ≈ 125.66 |
This chart shows how rpm values close to 1200 translate into radians/sec, helping you see the relationship at a glance.
Related Conversion Questions
- What is 1200 rpm in radians per second for different types of machinery?
- How do I convert revolutions per minute to radians/sec in a physics problem?
- Why does multiplying rpm by π/30 give radians per second?
- Can I convert 1200 rpm to radians per hour?
- What is the radian equivalent of 1200 rpm in rotational dynamics?
- How is rpm related to angular velocity in radians/sec?
- What is the purpose of converting rpm to radians per second?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns an object makes in a minute. It describes rotational speed, with higher rpm indicating faster rotation, commonly used in engines, motors, and machinery to specify their operational speed.
rad
Rad, short for radians, is a unit of angular measurement representing the angle created when the arc length equals the radius. One full circle equals 2π radians, making radians a natural measure for angles in mathematics and physics.
Conversion FAQs
How accurate is the conversion from rpm to radians per second?
The conversion is precise when using the exact formula: rpm * (2π / 60). Minor differences occur due to rounding π, but for most practical purposes, the results are accurate enough for engineering and scientific calculations.
Can I convert radians/sec back to rpm using the same formula?
Yes, reversing the process involves multiplying radians/sec by 60 and dividing by 2π, or equivalently, radians/sec * (30 / π). This allows you to switch between the two units depending on your needs.
Why is π used in the conversion process?
π appears because a full rotation, or circle, measures 2π radians. Since rpm counts revolutions, multiplying by 2π converts revolutions into radians, and dividing by 60 adjusts for seconds, linking the units effectively.