Tangential Acceleration Calculator

Physics overview

What is tangential acceleration?

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

Formula

Tangential acceleration formula

Tangential Velocityaₜ = rα

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: aₜ = rα.
Substitute the values: v = 4 × 3.
Calculate tangential acceleration: v = 12 m/s².

Rearranged equations

Solve for radius or angular acceleration

Radius

r = v ÷ ω

Divide tangential acceleration by angular acceleration.

Angular acceleration

ω = v ÷ r

Divide tangential acceleration by radius.

Physical relationship

Radius and rotation rate both affect v

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

Units

Standard SI units

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

Real-world applications

Where tangential acceleration 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 acceleration must be entered in radians per second squared.
Direction is not represented.
Units are not converted automatically.

Related tools

Use the Angular Acceleration Calculator to calculate angular acceleration, displacement, or time.

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

Questions and answers