Elara BennettThe conversion of 3 Hz to angular velocity results in approximately 18.8496 radians per second. This means that a frequency of 3 cycles per second corresponds to a rotation rate of about 18.85 radians each second.
To convert Hz to angular velocity, you need to multiply the frequency in Hz by 2π, because one cycle equals 2π radians. So, 3 Hz times 2π gives the angular speed in radians per second, which is 3 × 2 × 3.1416 = 18.8496 radians/sec. This calculation converts the number of cycles per second into the total angle rotated in radians per second.
Conversion Result
Conversion Tool
Result in angular:
Conversion Formula
The formula to convert frequency in Hz to angular velocity in radians per second is: angular velocity = frequency × 2π. This works because a full cycle of a wave or rotation equals 2π radians, and multiplying by 2π converts cycles per second into radians per second. For example, if you have 5 Hz, then: 5 × 2π = 31.4159 radians/sec.
Conversion Example
- Convert 10 Hz to angular velocity:
- Multiply 10 by 2π.
- 10 × 2 × 3.1416 = 62.832 radians/sec.
- This means a 10 Hz frequency equals about 62.832 radians per second.
- Convert 1.5 Hz:
- 1.5 × 2π = 1.5 × 6.2832 = 9.4248 radians/sec.
- This is how fast something rotates if it spins 1.5 cycles each second.
- Convert 0.5 Hz:
- 0.5 × 2π = 0.5 × 6.2832 = 3.1416 radians/sec.
- A half cycle per second equals approximately 3.1416 radians per second.
Conversion Chart
| Hz | Angular (radians/sec) |
|---|---|
| -22.0 | -138.2304 |
| -20.0 | -125.6640 |
| -18.0 | -113.0976 |
| -16.0 | -100.5312 |
| -14.0 | -87.9648 |
| -12.0 | -75.3984 |
| -10.0 | -62.8320 |
| -8.0 | -50.2656 |
| -6.0 | -37.6992 |
| -4.0 | -25.1328 |
| -2.0 | -12.5664 |
| 0.0 | 0.0000 |
| 2.0 | 12.5664 |
| 4.0 | 25.1328 |
| 6.0 | 37.6992 |
| 8.0 | 50.2656 |
| 10.0 | 62.8320 |
| 12.0 | 75.3984 |
| 14.0 | 87.9648 |
| 16.0 | 100.5312 |
| 18.0 | 113.0976 |
| 20.0 | 125.6640 |
| 22.0 | 138.2304 |
| 28.0 | 175.9296 |
Use this chart to quickly find the angular velocity for any given Hz value by locating the Hz in the first column and reading across to find the radians per second.
Related Conversion Questions
- How many radians per second is 3 Hz?
- What is the angular velocity in radians/sec for a frequency of 3 Hz?
- Convert 3 Hz to radians per second, what is the result?
- If something rotates at 3 Hz, how many radians does it turn in one second?
- How do I convert a frequency of 3 Hz into an angular measurement?
- What is the angular speed corresponding to 3 Hz?
Conversion Definitions
Hz
Hz, or Hertz, measures how many cycles or oscillations occur each second, representing frequency. It is a basic unit in physics and engineering to describe how often a repeating event, like a wave or rotation, happens in one second.
Angular
Angular refers to measurements of rotation or position in terms of angles, usually in radians, which quantify the amount of turn or rotation around a circle or axis. It describes how far something has rotated from a starting point in a circular path.
Conversion FAQs
How is Hz related to angular velocity?
Hz indicates how many complete cycles happen per second, while angular velocity in radians per second shows the rate of rotation in angles. The relationship is direct: multiply Hz by 2π to get radians/sec, because one cycle equals 2π radians.
Can I convert any Hz value to radians per second using this method?
Yes, by multiplying any frequency in Hz by 2π, you convert it to angular velocity in radians per second. This is valid for all positive and negative Hz values, representing forward or reverse rotation.
What does negative Hz mean in rotation conversion?
Negative Hz signifies rotation in the opposite direction, but when converting to radians per second, the magnitude is what matters; the negative indicates direction, not the size of the angular velocity.
Why use 2π in the conversion?
Because a full cycle of oscillation or rotation equals 2π radians, multiplying Hz by 2π converts the number of cycles per second into the total radians rotated per second, giving the angular speed.
