Linear Velocity to Angular Velocity Calculator

Ever wondered how fast a wheel spins when a car moves? That’s where linear velocity and angular velocity come in. If you need a quick way to convert between the two, our Linear Velocity to Angular Velocity Calculator makes it easy.

What’s Linear and Angular Velocity?

• Linear velocity (v) is how fast something moves in a straight line. Think of a car on a road.
• Angular velocity (ω) is how fast something spins. Picture a wheel turning.

They’re connected by a simple formula:

ω = v / r

Where:

• ω (omega) = Angular velocity (rad/s)
• v = Linear velocity (m/s)
• r = Radius (m)

A bigger radius means a slower spin for the same speed.

How to Use the Calculator

It’s super simple:

1. Enter the linear velocity (v) – how fast the object moves.
2. Choose the unit – meters per second (m/s), kilometers per hour (km/h), etc.
3. Enter the radius (r) – distance from the center to the edge.
4. Hit ‘Calculate’ – you’ll see the angular velocity in radians per second (rad/s), degrees per second (°/s), and RPM.

Example Calculation

A bike tire moves at 20 m/s, with a radius of 5 m.

Using the formula:

ω = 20 / 5 = 4 rad/s

Conversions:

• Degrees per second: 4 × (180 / π) = 229.18°/s
• Revolutions per minute (RPM): 4 × (60 / 2π) = 38.2

Quick Reference Table

Why This Matters

Ever seen a Ferris wheel? The outer seats move faster than the center. That’s linear velocity at work! But every part of the wheel spins at the same angular velocity.

FAQs

How do you convert linear velocity to angular velocity?

Use the formula ω = v / r. Divide the speed by the radius.

What’s the formula for angular velocity?

ω = v / r, where v is speed and r is radius.

Can I convert angular velocity back to linear?

Yep! Just multiply: v = ω × r.

Why use radians instead of degrees?

Radians make math easier. They’re the natural unit for circles.

Final Thoughts

Our Linear Velocity to Angular Velocity Calculator takes the hassle out of conversions. Just enter the values and get instant results. Whether you're solving physics problems or working on engineering projects, this tool saves time.