Calculators
Angular Acceleration Calculator
Solve constant angular-acceleration motion and rotational velocity changes.
Angular Acceleration Calculator tool
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About This Tool
Angular acceleration measures how quickly angular velocity changes with time. This calculator solves the constant-angular-acceleration relationship between initial angular velocity, final angular velocity, elapsed time, and angular acceleration. It supports radians per second, degrees per second, RPM, and common time units, so it is useful for rotational-motion exercises and straightforward speed-change estimates without manually converting every input first.
How To Use It
- Choose whether to solve for angular acceleration, final angular velocity, initial angular velocity, or elapsed time.
- Enter the three known quantities and select the units attached to each value.
- Use positive and negative signs consistently to represent your chosen direction of rotation and whether angular velocity increases or decreases.
- Read the result together with the displayed equation, and confirm that constant angular acceleration is a reasonable assumption for the interval you are modeling.
Examples
Speeding up from rest
A wheel changing from 0 to 10 rad/s in 2 s has α = (10 − 0)/2 = 5 rad/s².
Rotational deceleration
Changing from 10 rad/s to 4 rad/s in 3 s gives α = (4 − 10)/3 = −2 rad/s² when the original rotation direction is positive.
RPM change
A rotor increasing from 0 to 60 RPM in 2 s changes by 2π rad/s, giving an average constant angular acceleration of π rad/s².
Solve final angular velocity
Starting at 2 rad/s with α = 3 rad/s² for 4 s gives ω₂ = 2 + 3 × 4 = 14 rad/s.
Useful Notes
Core equation
For constant angular acceleration, α = (ω₂ − ω₁)/Δt. Rearranging the same relationship gives ω₂ = ω₁ + αΔt, ω₁ = ω₂ − αΔt, and Δt = (ω₂ − ω₁)/α.
Direction and negative values
Angular velocity and angular acceleration are directional quantities. In a one-axis problem, choose one rotation direction as positive. Negative acceleration does not always mean the object is slowing down; whether speed rises or falls depends on the signs of velocity and acceleration together.
Angular versus linear acceleration
Angular acceleration describes change in rotational rate and uses units such as rad/s². Linear tangential acceleration at a point also depends on its distance from the rotation axis, so angular acceleration alone does not specify a point's linear acceleration.
RPM and radians
RPM is convenient for rotating machinery, while SI rotational equations commonly use radians. One revolution equals 2π radians and 60 RPM equals one revolution per second, or 2π rad/s.
Constant-acceleration limitation
The equations here assume angular acceleration stays constant over the entered interval. Motors, braking systems, and real mechanisms can have acceleration that changes with time, load, control input, friction, or speed; those cases require a time-varying model or measured data.
FAQ
What is the formula for angular acceleration?
For a constant or average rate over an interval, angular acceleration is α = (ω₂ − ω₁)/Δt, where ω₁ and ω₂ are initial and final angular velocity.
What units does angular acceleration use?
The SI unit is radians per second squared (rad/s²). This calculator can also express it as degrees per second squared or RPM per second.
Can angular acceleration be negative?
Yes. Its sign indicates direction according to your chosen convention. A negative value often describes deceleration when angular velocity is positive, but sign and speed change should be interpreted together.
Is this the same as centripetal acceleration?
No. Angular acceleration describes a change in angular velocity. Centripetal acceleration points toward the rotation center and can exist even when angular speed is constant.
Does the calculator work when acceleration changes during the interval?
The result from velocity change divided by time is an average angular acceleration. The rearranged constant-acceleration equations should not be treated as an exact time-varying motion model.