Enter the linear velocity, angular velocity, and radius into the calculator to determine the missing variable.
Radians Per Second To Meters Per Second Formula
The following formula is used to calculate the linear velocity from angular velocity and radius.
v = \omega \cdot r
Variables:
- v is the linear velocity in meters per second (m/s)
- ω is the angular velocity in radians per second (rad/s)
- r is the radius in meters (m)
To calculate the linear velocity, multiply the angular velocity by the radius.
| Angular Velocity (rad/s) | Linear Velocity (m/s) |
|---|---|
| 0.5 | 0.250 |
| 1 | 0.500 |
| 2 | 1.000 |
| 3 | 1.500 |
| 5 | 2.500 |
| 6.283 | 3.142 |
| 10 | 5.000 |
| 12.566 | 6.283 |
| 15 | 7.500 |
| 20 | 10.000 |
| 25 | 12.500 |
| 31.416 | 15.708 |
| 40 | 20.000 |
| 50 | 25.000 |
| 62.832 | 31.416 |
| 75 | 37.500 |
| 100 | 50.000 |
| 125 | 62.500 |
| 150 | 75.000 |
| 200 | 100.000 |
| * Rounded to 3 decimals. Assumes constant radius r = 0.50 m. Formula: v = ω × r. | |
What is Radians Per Second To Meters Per Second?
The conversion from radians per second to meters per second is a way to translate angular velocity into linear velocity. This is particularly useful in scenarios involving rotational motion, where you need to determine the speed of a point on the edge of a rotating object. The linear velocity is directly proportional to both the angular velocity and the radius of the rotation.
How to Calculate Radians Per Second To Meters Per Second?
The following steps outline how to calculate the linear velocity from angular velocity and radius.
- First, determine the angular velocity (ω) in radians per second.
- Next, determine the radius (r) in meters.
- Finally, calculate the linear velocity using the formula v = ω * r.
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Angular velocity (ω) = 10 rad/s
Radius (r) = 2 m
Linear velocity (v) = 20 m/s