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120 rpm equals approximately 12.5664 radians per second
Converting 120 rpm to radians involves multiplying the rotations per minute by a factor to convert revolutions into radians and minutes into seconds. The result shows how many radians are swept out in one second when rotating at 120 rpm.
Introduction
When a object spins at 120 revolutions per minute, it covers a certain angle in radians per second. Since one revolution equals 2π radians, we need to convert rpm into radians per second by applying the correct formulas and steps. This helps in understanding rotation speeds in different units.
Conversion Tool
Result in rad:
Conversion Formula
The conversion from rpm to radians per second uses the formula: radians/sec = rpm * (2π) / 60. Why? Because each revolution is 2π radians, and there are 60 seconds in a minute. Multiplying rpm by 2π converts revolutions into radians, then dividing by 60 adjusts for seconds.
For example, for 120 rpm: 120 * 2π / 60 = 120 * 6.2832 / 60 = 12.5664 radians/sec. This calculation shows exactly how many radians are covered each second at that speed.
Conversion Example
- Convert 60 rpm:
- Multiply 60 by 2π: 60 * 6.2832 = 376.99
- Divide that by 60: 376.99 / 60 = 6.2832 rad/sec
- Convert 90 rpm:
- 90 * 2π = 565.49
- 565.49 / 60 = 9.4248 rad/sec
- Convert 150 rpm:
- 150 * 2π = 942.48
- 942.48 / 60 = 15.708 rad/sec
- Convert 200 rpm:
- 200 * 2π = 1256.64
- 1256.64 / 60 = 20.944 rad/sec
Conversion Chart
| RPM | Radians/sec |
|---|---|
| 95.0 | 9.9581 |
| 100.0 | 10.472 |
| 105.0 | 11.006 |
| 110.0 | 11.540 |
| 115.0 | 12.074 |
| 120.0 | 12.566 |
| 125.0 | 13.101 |
| 130.0 | 13.635 |
| 135.0 | 14.169 |
| 140.0 | 14.703 |
| 145.0 | 15.237 |
Use this chart to quickly find the radians per second for any rpm value between 95 and 145. Find the rpm in the first column and read across to see the rad/sec value.
Related Conversion Questions
- How many radians per second are in 120 rpm?
- What is the rad/sec equivalent of 120 rpm?
- Convert 120 revolutions per minute into radians per second?
- At 120 rpm, how many radians does an object sweep per second?
- Is 120 rpm equal to approximately 12.57 radians per second?
- How do I change 120 rpm into angular velocity in radians?
- What is the rad/sec value for a motor spinning at 120 rpm?
Conversion Definitions
rpm stands for revolutions per minute, measuring how many full turns an object makes in one minute. Rad is short for radians, a unit measuring angles, where one full revolution equals 2π radians, making it a standard for angular measurement in mathematics and physics.
Rad/sec, or radians per second, indicates how many radians an object rotates through each second. It’s a measure of angular velocity, helping to compare rotational speeds between different systems, especially when dealing with continuous rotation or oscillation.
Conversion FAQs
How do I convert 120 rpm into radians per second manually?
To convert 120 rpm into radians per second, multiply 120 by 2π and then divide by 60. This accounts for the radians in a revolution and seconds in a minute, giving the angular velocity in radians/sec.
Why is it necessary to divide by 60 in the formula?
Dividing by 60 adjusts for the number of seconds in a minute, converting the rotation rate from per minute to per second, which is the standard time unit used in radians/sec calculations.
Can I use this conversion for any rpm value?
Yes, the formula works for any rpm value. Just replace 120 with your desired rpm in the formula: radians/sec = rpm * 2π / 60, to find the angular velocity in radians per second.
What is the significance of radians in rotational movement?
Radians provide a natural measure of angles, directly related to the length of the arc of a circle. They simplify calculations in rotational movement, especially when dealing with angular displacement, velocity, and acceleration.
