Angular Acceleration Calculator
Calculate angular acceleration from change in angular velocity and time for rotational kinematics problems.
What Is Angular Acceleration?
Angular acceleration describes how quickly angular velocity changes over time. A spinning wheel that speeds up, slows down, or reverses direction has nonzero angular acceleration. It is the rotational analog of linear acceleration.
Angular Acceleration Formula
$$ \alpha = \frac{\omega_f - \omega_i}{t} $$\(\omega_i\) and \(\omega_f\) are initial and final angular velocities, and \(t\) is the elapsed time. In SI units, \(\alpha\) is in rad/s\(^2\). Positive \(\alpha\) means the object spins faster in the positive direction.
To convert RPM to rad/s, multiply by \(2\pi/60\). For example, 600 RPM equals about 62.8 rad/s.
Real-World Examples
A car engine ramping from idle to redline, a figure skater pulling arms inward, and an electric motor starting from rest all involve angular acceleration. Knowing \(\alpha\) helps predict how long a rotation takes to reach a target speed.
Related tools: Angular Displacement Calculator and Centripetal Acceleration Calculator.
Frequently Asked Questions
Can angular acceleration be negative?
Yes. A negative value means angular velocity is decreasing or the spin direction is reversing, depending on your sign convention.
What is the difference between rad/s and RPM?
RPM counts revolutions per minute. Rad/s measures radians per second. One revolution equals \(2\pi\) radians.
Does this formula require constant acceleration?
The formula gives average angular acceleration over the interval. It is exact when acceleration is constant and a good estimate for small intervals otherwise.
How does angular acceleration relate to torque?
For a rigid body, net torque equals moment of inertia times angular acceleration: \(\tau = I\alpha\). This is the rotational form of Newton's second law.
What if initial and final velocities use the same unit?
Select rad/s or RPM once for both inputs. The calculator converts internally to rad/s before applying the formula.
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