15 rpm is approximately 1.57 radians per second.
This conversion is based on the fact that one revolution per minute (rpm) equals 2π radians divided by 60 seconds. So, multiplying 15 rpm by this factor gives the radians per second rate, which measures how many radians are covered each second at that rotation speed.
Conversion Result
Result in rad:
Conversion Formula
The formula to convert revolutions per minute (rpm) to radians per second (rad/sec) is: rpm × (2π / 60). It works because one full rotation is 2π radians, and there are 60 seconds in a minute. Multiplying rpm by this factor gives the radians covered every second, which is rad/sec.
For example, converting 15 rpm: 15 × (2π / 60) = (15 × 6.2832) / 60 = 94.248 / 60 = 1.5708 rad/sec. This step-by-step calculation confirms the conversion process and ensures accuracy.
Conversion Example
- Convert 20 rpm to rad/sec: 20 × (2π / 60) = (20 × 6.2832) / 60 = 125.664 / 60 = 2.0944 rad/sec.
- Convert 5 rpm to rad/sec: 5 × (2π / 60) = (5 × 6.2832) / 60 = 31.416 / 60 = 0.5236 rad/sec.
- Convert 50 rpm to rad/sec: 50 × (2π / 60) = (50 × 6.2832) / 60 = 314.16 / 60 = 5.236 rad/sec.
- Convert 100 rpm to rad/sec: 100 × (2π / 60) = (100 × 6.2832) / 60 = 628.32 / 60 = 10.472 rad/sec.
- Convert 0 rpm to rad/sec: 0 × (2π / 60) = 0, as zero rotations per minute means no movement.
Conversion Chart
This table shows the radian equivalent for rpm values from -10.0 to 40.0. Negative values indicate reverse rotation, while positive values are forward. Use this chart to quickly find the radians per second for different rpm speeds.
| rpm | rad/sec |
|---|---|
| -10.0 | -1.0472 |
| -9.0 | -0.9425 |
| -8.0 | -0.8378 |
| -7.0 | -0.7331 |
| -6.0 | -0.6283 |
| -5.0 | -0.5236 |
| -4.0 | -0.4189 |
| -3.0 | -0.3142 |
| -2.0 | -0.2094 |
| -1.0 | -0.1047 |
| 0.0 | 0.0 |
| 1.0 | 0.1047 |
| 2.0 | 0.2094 |
| 3.0 | 0.3142 |
| 4.0 | 0.4189 |
| 5.0 | 0.5236 |
| 6.0 | 0.6283 |
| 7.0 | 0.7331 |
| 8.0 | 0.8378 |
| 9.0 | 0.9425 |
| 10.0 | 1.0472 |
| 15.0 | 1.5708 |
| 20.0 | 2.0944 |
| 25.0 | 2.6179 |
| 30.0 | 3.1416 |
| 35.0 | 3.6652 |
| 40.0 | 4.1888 |
Related Conversion Questions
- How do I convert 15 rpm to radians per second for a rotating motor?
- What is the radian equivalent of 15 rpm in angular velocity?
- Can I quickly find radians per second from rpm values like 15 rpm?
- What is the formula to change 15 rpm into rad/sec?
- How many radians does a 15 rpm rotation cover in one second?
- Is there an easy way to convert rpm to radians for 15 rpm?
- What is the rad/sec value for a wheel spinning at 15 rpm?
Conversion Definitions
rpm, revolutions per minute, measures how many complete rotations an object makes in one minute. It is a rotational speed describing how fast something spins. The higher the rpm, the faster the object rotates around its axis.
Rad, short for radians, is a unit measuring angles based on the radius of a circle. One radian equals about 57.2958 degrees, and it represents the angle formed when arc length equals radius length, used to quantify angles in circular motion.
Conversion FAQs
How do I convert 15 rpm to radians per second manually?
Multiply 15 by 2π and then divide by 60. So, 15 × 6.2832 / 60 equals approximately 1.57 rad/sec. This method gives you the radians covered each second based on the rpm value.
Why is there a 2π factor in the conversion?
The 2π factor represents the total radians in a full circle, which is the measure of one revolution. Multiplying rpm by 2π converts revolutions into radians, allowing the measurement of rotational speed in radians per second.
Can I use this conversion for any rpm value?
Yes, the formula applies universally. Just replace the rpm value with your number and multiply by 2π/60 to get radians per second. The calculation remains the same regardless of the rpm size.
What is the significance of radians in rotational motion?
Radians offer a natural way to measure angles because they relate arc length to radius directly. In rotational motion, using radians simplifies formulas for angular velocity, acceleration, and other parameters, making calculations more straightforward.
How does negative rpm affect the radian conversion?
Negative rpm indicates reverse rotation, so converting it to radians per second yields a negative value, representing direction. The magnitude remains the same, but the negative sign shows the rotation’s opposite direction.