Tangential Velocity Calculator

Physics overview

What is tangential velocity?

Tangential velocity is the linear speed of an object moving along the edge of a circular path.

Formula

Tangential velocity formula

Tangential Velocityv = rω

v is tangential velocity in m/s.
r is radius in meters.
ω is angular velocity in rad/s.

Worked example

A point is 4 m from the axis and rotates at 3 rad/s

Write the formula: v = rω.
Substitute the values: v = 4 × 3.
Calculate tangential velocity: v = 12 m/s.

Rearranged equations

Solve for radius or angular velocity

Radius

r = v ÷ ω

Divide tangential velocity by angular velocity.

Angular velocity

ω = v ÷ r

Divide tangential velocity by radius.

Physical relationship

Radius and rotation rate both affect v

Tangential velocity increases when radius increases, angular velocity increases, or both increase.

Units

Standard SI units

Use meters per second for tangential velocity, meters for radius, and radians per second for angular velocity.

Real-world applications

Where tangential velocity is used

Wheels, gears, and rotating disks.
Turbines and mechanical shafts.
Amusement rides and rotating platforms.
Planetary and satellite motion.
Motors and industrial machinery.

Calculation limits

Important assumptions

All entered values must be greater than zero.
Radius is measured from the rotation axis.
Angular velocity must be entered in radians per second.
Direction is not represented.
Units are not converted automatically.

Related tools

Use the Angular Velocity Calculator to calculate angular velocity, displacement, or time.

Use the Centripetal Acceleration Calculator to calculate inward acceleration in circular motion.

Questions and answers