m/s to rad/s & rad/s to m/s Calculations
To convert between linear speed (meters per second, m/s) and angular speed (radians per second, rad/s), use the following formulas:
- Linear Speed to Angular Speed: Rad/s = (m/s) ÷ (Radius in meters)
- Angular Speed to Linear Speed: m/s = (Rad/s) × (Radius in meters)
Where:
- m/s is the linear speed in meters per second.
- rad/s is the angular speed in radians per second.
- Radius is the distance from the center of rotation, measured in meters or other units.
Conversion Examples
Example 1: Convert 20 m/s to rad/s (with a radius of 2 meters)
Using the formula: Rad/s = 20 ÷ 2 Rad/s = 10
Result: 20 m/s is equal to 10 rad/s for a 2-meter radius.
Example 2: Convert 15 rad/s to m/s (with a radius of 3 meters)
Using the formula: m/s = 15 × 3 m/s = 45
Result: 15 rad/s is equal to 45 m/s for a 3-meter radius.
Unit Conversion Table
| Radius Unit | 1 Meter (m) | 1 Centimeter (cm) | 1 Millimeter (mm) | 1 Kilometer (km) | 1 Inch (in) | 1 Foot (ft) | 1 Yard (yd) | 1 Mile (mi) |
|---|---|---|---|---|---|---|---|---|
| Meters (m) | 1 | 0.01 | 0.001 | 1000 | 0.0254 | 0.3048 | 0.9144 | 1609.34 |
| Centimeters (cm) | 100 | 1 | 0.1 | 100000 | 2.54 | 30.48 | 91.44 | 160934 |
| Millimeters (mm) | 1000 | 10 | 1 | 1,000,000 | 25.4 | 304.8 | 914.4 | 1,609,344 |
| Kilometers (km) | 0.001 | 0.00001 | 0.000001 | 1 | 0.0000254 | 0.0003048 | 0.0009144 | 1.609 |
| Inches (in) | 39.37 | 0.3937 | 0.03937 | 39370.1 | 1 | 12 | 36 | 63360 |
| Feet (ft) | 3.2808 | 0.0328 | 0.00328 | 3280.84 | 0.0833 | 1 | 3 | 5280 |
| Yards (yd) | 1.0936 | 0.0109 | 0.00109 | 1093.61 | 0.0278 | 0.3333 | 1 | 1760 |
| Miles (mi) | 0.000621 | 0.00000621 | 0.000000621 | 0.62137 | 0.000016 | 0.000189 | 0.000568 | 1 |
Quick Reference Calculations
- 10 m/s to rad/s (radius = 2 meters): 10 ÷ 2 = 5 rad/s
- 50 rad/s to m/s (radius = 1.5 meters): 50 × 1.5 = 75 m/s
- 30 m/s to rad/s (radius = 5 feet, converted to 1.524 meters): 30 ÷ 1.524 = 19.7 rad/s
- 12 rad/s to m/s (radius = 10 inches, converted to 0.254 meters): 12 × 0.254 = 3.048 m/s
Summary
- To convert m/s to rad/s, divide by the radius.
- To convert rad/s to m/s, multiply by the radius.
- Ensure the radius is in compatible units such as meters, centimeters, or inches for accurate calculations.
- Use the unit conversion table above to switch between different radius measurements.
FAQs
- How do I convert m/s to rad/s?
To convert meters per second (m/s) to radians per second (rad/s), divide the linear speed by the radius: Rad/s = (m/s) ÷ (Radius in meters). - How do I convert rad/s to m/s?
To convert radians per second (rad/s) to meters per second (m/s), multiply the angular speed by the radius: m/s = (Rad/s) × (Radius in meters). - Does the radius need to be in meters for accurate conversion?
The radius can be in any unit, but it should be converted to meters for accurate calculations. Use the unit conversion table to switch between different radius measurements. - What happens if I change the radius unit after calculation?
If the radius unit is changed, the result will automatically update to reflect the new unit, ensuring consistency in conversions. - Can I use this calculator for different units like inches, feet, or kilometers?
Yes, the calculator supports various units for radius, including meters, centimeters, millimeters, inches, feet, yards, and miles. The unit selection ensures correct conversion factors are applied.
