Mechanics
Linear-Angular Velocity Relation
Relates linear and angular velocities.
Variables
vm/s
Linear velocity
Tangential speed
rm
Radius
Distance from axis
Allowed values: greater than 0
ωrad/s
Angular velocity
Rate of rotation
Derivation
Arc length s = rθ, differentiate: v = ds/dt = r(dθ/dt) = rω.
Your notes
0/5000
Check value
Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- r = 2 m (Radius)
- ω = 3 rad/s (Angular velocity)
Result: v = 6 m/s
Other mechanics formulas with the same quantities
- Centripetal Force (Rotational Motion) shares Radius
- Rotational Kinetic Energy (Rotational Motion) shares Angular velocity
- Angular Momentum (Rotational Motion) shares Angular velocity
- Rolling Kinetic Energy (Rotational Motion) shares Angular velocity
Where this formula is listed
- Mechanics formulas, under Rotational Motion, alongside Angular Acceleration, Torque, Moment of Inertia (Point Mass), Newton's Second Law (Rotation) and Rotational Kinematic 1.
- In the mechanics list it comes after Angular Acceleration and before Centripetal Acceleration.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Linear-Angular Velocity Relation formula?
Linear-Angular Velocity Relation is written v = rω. Relates linear and angular velocities. It belongs to Mechanics, under Rotational Motion.
What are the units in v = rω?
In SI units, v is linear velocity, measured in m/s; r is radius, measured in m; ω is angular velocity, measured in rad/s.
How is the Linear-Angular Velocity Relation formula derived?
Arc length s = rθ, differentiate: v = ds/dt = r(dθ/dt) = rω. The result is v = rω.