Elara BennettThe result of converting 5 rpm to radians per second is approximately 0.5236 rad/sec.
To understand this, note that rpm (revolutions per minute) measures how many full turns something makes each minute, while radians per second indicates the angular distance covered every second. The conversion involves changing minutes to seconds and revolutions to radians, using the fact that one revolution equals 2π radians.
Conversion Result
5 rpm is equal to about 0.5236 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 one complete revolution equals 2π radians, and there are 60 seconds in a minute, so dividing by 60 converts minutes to seconds. Multiplying rpm by 2π gives radians per minute, then dividing by 60 gives radians per second.
For example, with 5 rpm: 5 * (2π) / 60 = (5 * 6.2832) / 60 = 31.416 / 60 = 0.5236 rad/sec.
Conversion Example
- Convert 10 rpm:
- Multiply 10 by 2π: 10 * 6.2832 = 62.832
- Divide by 60: 62.832 / 60 = 1.0472 rad/sec
- Convert 15 rpm:
- 15 * 6.2832 = 94.248
- 94.248 / 60 = 1.5708 rad/sec
- Convert 20 rpm:
- 20 * 6.2832 = 125.664
- 125.664 / 60 = 2.0944 rad/sec
- Convert 25 rpm:
- 25 * 6.2832 = 157.08
- 157.08 / 60 = 2.618 rad/sec
- Convert 30 rpm:
- 30 * 6.2832 = 188.496
- 188.496 / 60 = 3.1416 rad/sec
Conversion Chart
This chart shows how rpm values convert to radians per second from -20.0 to 30.0. Use this to quickly see the approximate rad/sec for a given rpm. Negative values indicate reverse rotation, positive for forward rotation.
| rpm | rad/sec |
|---|---|
| -20.0 | -2.0944 |
| -10.0 | -1.0472 |
| 0.0 | 0.0 |
| 5.0 | 0.5236 |
| 10.0 | 1.0472 |
| 15.0 | 1.5710 |
| 20.0 | 2.0944 |
| 25.0 | 2.6180 |
| 30.0 | 3.1416 |
Related Conversion Questions
- How many radians per second is 5 rpm equivalent to in a rotating motor?
- What is the rad/sec value for a device spinning at 5 rpm?
- Can you convert 5 rpm into radians per second for physics calculations?
- What is the angular velocity in radians/sec for 5 revolutions per minute?
- How do I convert a rotational speed of 5 rpm into radians per second?
- What is the rad/sec equivalent for 5 rpm in engineering contexts?
- How many radians per second does 5 rpm correspond to in mechanical systems?
Conversion Definitions
rpm (revolutions per minute) measures how many complete turns an object makes each minute, used in machinery and engines to indicate rotational speed. Rad (radian) is a unit of angular measure, representing the angle created by an arc equal in length to the radius of a circle.
Rad/sec (radians per second) indicates the rate at which an object rotates around a circle, showing how many radians it covers each second, essential in physics and engineering for describing angular velocity.
Conversion FAQs
How does changing rpm affect rad/sec?
Increasing rpm linearly increases rad/sec because the conversion formula directly multiplies rpm by 2π/60. Doubling rpm doubles rad/sec, making the relationship straightforward and proportional.
Is the conversion from rpm to rad/sec the same for all rotational speeds?
Yes, the formula applies universally regardless of the rpm value. Whether it’s 1 rpm or 1000 rpm, multiplying by 2π/60 gives the corresponding rad/sec.
Why do we divide by 60 in the formula?
Dividing by 60 converts minutes to seconds because rpm measures revolutions per minute, and radians per second require seconds as the time unit. This ensures the angular velocity is expressed per second.
Can this conversion be used for negative rpm values?
Yes, negative rpm indicates reverse rotation. Applying the same formula yields negative rad/sec, accurately representing the direction of rotation.
What practical applications use rpm to rad/sec conversions?
Conversions are used in motor design, physics experiments, rotational machinery, and robotics to determine angular velocities, ensuring systems operate within safe and effective rotational speeds.
