The conversion of 3 Hz to angular velocity results in approximately 18.85 radians per second. This means that a frequency of 3 cycles per second correlates to an angular rotation of about 18.85 radians every second, indicating how fast something rotates in terms of angles.
To convert Hz to angular velocity, we multiply the frequency in hertz by 2π (approximately 6.2832). Since Hz measures cycles per second, and angular velocity measures radians per second, the formula involves the full circle (2π radians) for each cycle. Therefore, multiplying the frequency by 2π gives the angular velocity in radians/sec.
Conversion Result
Conversion Tool
Result in angular:
Conversion Formula
The formula to convert hertz to angular velocity relies on multiplying the frequency by 2π because a full rotation or cycle contains 2π radians. This stems from the relationship between cycles per second and radians per second. For example, if you have 3 Hz, multiply by 2π: 3 × 6.2832 = 18.8496 radians/sec. This math ensures that each cycle’s rotation in radians is accounted for, giving the angular velocity in radians per second.
Conversion Example
- Convert 5 Hz to angular:
- Step 1: Recognize the formula: radians/sec = Hz × 2π
- Step 2: Multiply 5 by 2π: 5 × 6.2832 = 31.416 radians/sec
- Step 3: Result: 5 Hz equals approximately 31.416 radians/sec
- Convert 1 Hz to angular:
- Step 1: Use the formula: radians/sec = 1 × 2π
- Step 2: Multiply 1 by 6.2832: 6.2832 radians/sec
- Step 3: Result: 1 Hz equals approximately 6.283 radians/sec
- Convert 10 Hz to angular:
- Step 1: Formula: radians/sec = 10 × 2π
- Step 2: Multiply 10 by 6.2832: 62.832 radians/sec
- Step 3: Result: 10 Hz corresponds to roughly 62.832 radians/sec
Conversion Chart
| Hz | Angular (radians/sec) |
|---|---|
| -22.0 | -138.23 |
| -20.0 | -125.66 |
| -18.0 | -113.10 |
| -16.0 | -100.53 |
| -14.0 | -87.96 |
| -12.0 | -75.40 |
| -10.0 | -62.83 |
| -8.0 | -50.27 |
| -6.0 | -37.70 |
| -4.0 | -25.13 |
| -2.0 | -12.57 |
| 0.0 | 0.00 |
| 2.0 | 12.57 |
| 4.0 | 25.13 |
| 6.0 | 37.70 |
| 8.0 | 50.27 |
| 10.0 | 62.83 |
| 12.0 | 75.40 |
| 14.0 | 87.96 |
| 16.0 | 100.53 |
| 18.0 | 113.10 |
| 20.0 | 125.66 |
| 22.0 | 138.23 |
| 24.0 | 150.80 |
| 26.0 | 163.36 |
| 28.0 | 175.93 |
Use this chart to quickly find the angular velocity in radians/sec for any Hz value in the range. Simply look across the row for the Hz value and read the corresponding radians/sec value.
Related Conversion Questions
- How many radians per second is 3 Hz?
- What is the angular velocity of 3 Hz in radians?
- How to convert a frequency of 3 Hz to radians/sec?
- Is 3 Hz equivalent to 18.85 radians/sec?
- What is the formula to change 3 Hz to angular measurement?
- How many radians does 3 Hz correspond to per second?
- Convert 3 Hz into angular velocity in radians/sec?
Conversion Definitions
Hz
Hz, or hertz, measures how many cycles or oscillations occur in one second. It is a frequency unit used to describe how fast a repeating event happens over time, directly relating to the rate of oscillation or rotation per second.
Angular
Angular, in this context, refers to angular velocity, which measures how quickly an object rotates around a point in radians per second. It quantifies the rate of change of an angle, representing rotational speed in a circular motion.
Conversion FAQs
How does increasing the Hz value affect the angular velocity?
As the Hz value increases, the angular velocity in radians/sec also increases proportionally because the formula multiplies Hz by 2π. This means a higher frequency results in faster rotation in terms of radians per second.
Can I convert angular velocity back to Hz?
Yes, to convert from radians/sec back to Hz, divide the angular velocity by 2π. This reverses the process, giving the number of cycles per second if you know the angular velocity in radians/sec.
What if I input a negative Hz value in the tool?
A negative Hz value indicates reverse rotation or oscillation in the opposite direction, but mathematically, the conversion to radians/sec will also be negative, reflecting the opposite rotational direction in angular velocity.
Is the conversion different for different units of angular measurement?
Yes, if you want to convert to degrees per second instead of radians per second, multiply Hz by 360° and then divide by 1 second, or directly convert using degrees. The current formula specifically converts to radians/sec, which is standard in many physics applications.