The conversion of 45 rpm to radians per second results in approximately 4.7124 rad/sec.
To convert revolutions per minute (rpm) to radians, you multiply the rpm value by 2π (approximately 6.2832) and divide by 60, because there are 2π radians in one revolution and 60 seconds in a minute. So, the formula is: radians/sec = rpm × 2π / 60.
What is 45 rpm in radians per second?
45 rpm equals about 4.7124 radians per second. This means that an object rotating at 45 revolutions each minute is turning through roughly 4.7124 radians every second. This conversion helps compare rotational speeds across different units by converting rpm into radians per second.
Conversion Tool
Result in rad:
Conversion Formula
The conversion formula is radians/sec = rpm × 2π / 60. It works because a revolution equals 2π radians, and since rpm indicates revolutions per minute, dividing by 60 converts it to per second. Multiplying by 2π gives the radians traveled each second.
For example, for 45 rpm:
- Start with 45 rpm
- Multiply by 2π (approximately 6.2832): 45 × 6.2832 = 282.743 radians per minute
- Divide by 60 seconds: 282.743 / 60 = 4.7124 radians per second
Conversion Example
Let’s convert 60 rpm into radians per second:
- Multiply 60 rpm by 2π: 60 × 6.2832 = 376.992 radians per minute
- Divide by 60: 376.992 / 60 = 6.2832 radians per second
This means 60 rpm equals approximately 6.2832 rad/sec.
Another example, 30 rpm:
- 30 × 6.2832 = 188.496 radians per minute
- Divide by 60: 188.496 / 60 = 3.1416 rad/sec
So, 30 rpm is about 3.1416 rad/sec.
Conversion Chart
This chart shows various rpm values and their rad/sec equivalents:
| rpm | rad/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 |
To use the chart, find your rpm value in the left column and read across to see the approximate radians per second in the right column.
Related Conversion Questions
- How many radians per second is 45 rpm?
- What is the rad/sec equivalent of 45 revolutions per minute?
- Convert 45 rpm to radians per second for a rotating motor?
- At what rad/sec does 45 rpm correspond in angular velocity?
- How do I change 45 rpm into radians for physics calculations?
- What is the angular velocity in radians/sec for 45 rpm?
- How can I convert rpm to radians per second for a spinning wheel?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns an object makes in one minute. It helps quantify rotational speed, often used for motors, engines, and spinning objects, indicating the frequency of rotation in a time unit of minutes.
rad
Rad, or radians, is a measure of angles based on the radius of a circle. One radian equals the angle created when the arc length equals the radius. It provides a natural way to measure rotation, with 2π radians representing a full circle.
Conversion FAQs
What is the significance of converting rpm to radians per second?
This conversion allows for easier comparison of rotational speeds across different units, especially in physics and engineering calculations involving angular velocity, torque, or rotational energy, which often use radians/sec.
Can I convert any rpm value to radians per second using the same formula?
Yes, the formula works universally for all rpm values because it directly relates revolutions to radians and accounts for seconds in a minute, ensuring consistent conversion regardless of the number used.
Why do we divide by 60 in the formula?
Dividing by 60 converts the rpm value from per-minute to per-second, which is necessary because radians per second is the standard unit for angular velocity in many scientific calculations.
Is there a difference between angular velocity in rpm and rad/sec?
Yes, rpm measures revolutions per minute, a rotational frequency, while rad/sec measures how many radians the object turns per second, a more direct measure of angular speed used in physics and engineering contexts.