Angular acceleration calculator
This angular acceleration calculator shows how fast an angular velocity changes. Example: speeding up from 0 to 20 rad/s in 4 s gives α = 5 rad/s².
Example: What is given: Initial and final angular velocity, time · Initial angular velocity ω₀ 0 rad/s · Final angular velocity ω₁ 20 rad/s · Time interval Δt 4 s → Result: α = 5 rad/s². Source: Halliday/Resnick/Walker, Fundamentals of Physics, Rotation (α = Δω/Δt, τ = Iα, a_t = αr). Updated: .
How it is calculated
Angular acceleration α tells you how much the angular velocity of a rotating body changes each second. It is the rotational counterpart of ordinary acceleration and is measured in rad/s².
Formulas
From two angular velocities: α = (ω₁ − ω₀) / Δt. From rotational dynamics: α = τ / I, where τ is the net torque and I the moment of inertia (the rotational version of F = m·a). Along the path: α = aₜ / r. At constant α the body sweeps the angle φ = ω₀·Δt + ½·α·Δt².
Worked example
A disc speeds up from 0 to 20 rad/s in 4 s. Then α = (20 − 0) / 4 = 5 rad/s², or 286.479 °/s². In that time it sweeps φ = ½ · 5 · 4² = 40 rad, which is 6.3662 revolutions. A torque of 10 N·m acting on a moment of inertia of 2 kg·m² gives the same α = 5 rad/s². A point at 0.5 m from the axis with aₜ = 3 m/s² corresponds to α = 6 rad/s².
- A negative result means slowing down, or speeding up against the chosen positive direction.
- Time, moment of inertia and radius must be greater than 0.
- The calculator assumes constant α; for a varying torque the result is an average.
Frequently asked questions
What is the difference between angular velocity and angular acceleration?
Angular velocity ω describes how fast the angle changes (rad/s). Angular acceleration α describes how fast ω itself changes (rad/s²).
How are torque and angular acceleration related?
Through the moment of inertia: τ = I·α. With the same torque, a body with a large I spins up more slowly. For I = 2 kg·m² and τ = 10 N·m, α = 5 rad/s².
How do I convert α to revolutions per second²?
Divide by 2π, because one revolution equals 2π rad. 5 rad/s² becomes 0.795775 rev/s².
Sources and legal basis
- Halliday/Resnick/Walker, Fundamentals of Physics, Rotation (α = Δω/Δt, τ = Iα, a_t = αr)
- Wikipedia – Winkelbeschleunigung
As of: · Editorial policy
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