Case 1
- Angular velocity (rad/s)
- 10rad/s
- Distance from the axis (m)
- 2m
20.000m/s
Open with these valuesTangential Velocity Calculator
20.000m/s
Result: 20.000 m/sTangential velocity is angular velocity times radius: a point 2 m from the axis turning at 10 rad/s moves at 20 m/s. The angular velocity goes in as radians per second — from rpm, divide by 60 and multiply by 2π. Every point of a rigid body shares the same ω, but the rim always moves faster than the hub.
The numbers at a glance
Held fixed: Angular velocity (rad/s) 10.000 rad/s.
| Distance from the axis (m) (m) | Result (m/s) |
|---|---|
| 0.000 | 0.000 |
| 0.500 | 5.000 |
| 1.000 | 10.000 |
| 1.500 | 15.000 |
| 2.000Your value | 20.000 |
| 2.500 | 25.000 |
| 3.000 | 30.000 |
| 3.500 | 35.000 |
| 4.000 | 40.000 |
Worked examples
Case 2
- Angular velocity (rad/s)
- 2.5rad/s
- Distance from the axis (m)
- 4m
10.000m/s
Open with these valuesCase 3
- Angular velocity (rad/s)
- 7rad/s
- Distance from the axis (m)
- 7m
49.000m/s
Open with these valuesHow it's calculated
v = ω × r
- StepConvert the rotation rate to rad/s: rpm ÷ 60 × 2π, or rev/s × 2π.
- StepEnter how far the point sits from the axis, in metres.
- ResultMultiply the two; the answer is in metres per second.
Reference table
| ω, radius | What that means | Tangential velocity |
|---|---|---|
| 0, 2 | At rest | 0 |
| 10, 0 | Spinning, but on the axis | 0 |
| 0.5, 0.5 | About 4.8 rpm | 0.25 |
| 2.5, 4 | About 23.9 rpm | 10 |
| 10, 2 | About 95.5 rpm | 20 |
| 7, 7 | About 66.8 rpm | 49 |
Questions
How do I calculate tangential velocity?
Multiply the angular velocity by the radius: v = ω × r. Radians per second times metres gives metres per second. A point 2 m from the axis spinning at 10 rad/s moves at 20 m/s.
My rotation rate is in rpm — what do I enter?
Divide the rpm by 60 to get revolutions per second, then multiply by 2π. So 3000 rpm is 314.159 rad/s. Typing rpm straight into the field overstates the speed by a factor of 9.55.
What is the difference between tangential and angular velocity?
Angular velocity in rad/s is the same for every point of a rigid body, while tangential velocity in m/s depends on the radius. A point twice as far from the axis moves twice as fast.
Why does the rim move faster than the hub?
Because tangential velocity is proportional to the radius. A point further out must cover a longer circle in the same time, so its linear speed is higher.
Can I start from the rotation frequency instead?
Yes. If you know the frequency f in revolutions per second, the angular velocity is ω = 2πf, so the tangential velocity is v = 2πrf. Convert rpm to rev/s by dividing by 60 first.
Sources and last check
Information, not professional advice.