The conversion of 400 rpm to radians per second results in approximately 41.89 rad/s. This means that an object rotating at 400 revolutions per minute is turning about 41.89 radians every second, a measure of rotational speed in radians rather than revolutions.
To convert rpm to rad/s, you multiply the revolutions per minute by 2π (since one revolution equals 2π radians) and divide by 60 (seconds in a minute). The formula is: (rpm) × (2π) / 60 = rad/s. For 400 rpm, it is (400 × 2π) / 60, which simplifies to approximately 41.89 radians per second. This calculation converts the rotational speed from a revolutions-based measure to radians-based measure, which is often used in physics and engineering.
Conversion Result
400 rpm equals approximately 41.89 radians per second.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to rad/sec is: (rpm) × (2π) / 60. It works because one revolution equals 2π radians, and there are 60 seconds in a minute. So, multiplying rpm by 2π gives radians per minute, then dividing by 60 converts to radians per second. For example, for 400 rpm:
- Multiply 400 by 2π: 400 × 6.2832 ≈ 2513.27 radians per minute.
- Divide 2513.27 by 60: 2513.27 / 60 ≈ 41.89 rad/sec.
Conversion Example
Let’s convert 600 rpm to rad/sec:
- Step 1: Multiply 600 by 2π: 600 × 6.2832 ≈ 3769.91 radians per minute.
- Step 2: Divide 3769.91 by 60: 3769.91 / 60 ≈ 62.83 rad/sec.
- This means 600 rpm is approximately 62.83 radians per second.
Conversion Chart
| rpm | Radians per second (rad/sec) |
|---|---|
| 375.0 | 39.27 |
| 380.0 | 39.80 |
| 385.0 | 40.33 |
| 390.0 | 40.86 |
| 395.0 | 41.39 |
| 400.0 | 41.89 |
| 405.0 | 42.42 |
| 410.0 | 42.94 |
| 415.0 | 43.47 |
| 420.0 | 44.00 |
| 425.0 | 44.52 |
This chart helps to quickly find the rad/sec equivalent for rpm values between 375 and 425. Read the first column for rpm and find the corresponding rad/sec in the second column.
Related Conversion Questions
- How many radians per second are in 400 rpm?
- What is the rad/sec equivalent of 400 revolutions per minute?
- How do I convert 400 rpm to angular velocity in radians?
- What is 400 rpm in radians per second for rotational physics calculations?
- Can you show me the formula to change 400 rpm into radians?
- What is the rad/sec value for a motor spinning at 400 rpm?
- How do I calculate radians per second from 400 rpm in engineering?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns an object makes each minute, used to describe rotational speeds in machines and engines, indicating how fast something spins around its axis in a minute.
rad
Radian (rad) is a unit of angular measure that describes the size of an angle based on the radius of a circle, with one radian being the angle where the arc length equals the radius, used in mathematics and physics to measure rotation.
Conversion FAQs
How is rpm related to radians per second?
Rpm measures how many complete rotations occur each minute, whereas radians per second quantify rotational speed in radians each second. To relate them, you convert revolutions to radians and adjust for time units, resulting in the formula (rpm) × (2π) / 60.
Why use radians instead of revolutions in calculations?
Radians provide a natural measure for angles in mathematical equations, especially in calculus and physics, because they relate directly to arc lengths and angular velocities, simplifying formulas involving rotational motion.
Can I convert rpm to radians per second without a calculator?
Yes, by knowing that 1 rpm equals approximately 0.10472 rad/sec, you can multiply rpm by this factor or use the formula directly if you remember the conversion steps. For 400 rpm, it’s about 41.89 rad/sec.
What real-world applications use rad/sec instead of rpm?
Rad/sec are used in engineering, physics, and robotics where precise measurement of angular velocity is required, such as in motor control, spacecraft rotation, and mechanical simulation.