Angular acceleration converter
Convert angular acceleration between rad/s² and the rpm-per-second that motor datasheets use.
That's 2.1× as quick as a ceiling fan, while a power drill is 19× quicker. Reaching 1,000 rpm from rest would take about 10 seconds.
What it means
How fast does it spin up?
Angular acceleration is torque divided by moment of inertia, so the same motor spins a light disc up far faster than a heavy one.
Every unit
Your acceleration in every unit
Learn
Three things worth knowing
-
1 rad/s² = 9.55 rpm per second
Because one rad/s is 9.549 rpm. A motor gaining 1,000 rpm a second is accelerating at 105 rad/s².
-
Torque over inertia
It is Newton’s second law for rotation: α = τ ÷ I. Halve the inertia and the same torque spins it up twice as fast, which is why flywheels are made light when they need to respond.
-
Not the same as speed
A hard drive at 7,200 rpm has a huge angular velocity and, once running, no angular acceleration at all. The acceleration is what happens during spin-up.
Shortcuts
Popular angular acceleration conversions
Background
About angular acceleration
The spinning counterpart of ordinary acceleration: how fast the rate of turning changes. Theory works in radians per second squared; motor datasheets quote rpm gained per second, and the two differ by a factor of 9.55.