Calculating Angular Acceleration w/ Torque & Moment of Inertia

[SDTK]

Homework Statement

this is a question just to help with my understanding: ...

when Torque (kg m^2/s^2) and the Moment of Inertia (kg m^2) are known and used to find angular acceleration, ... T(net)/I, are the units for the resulting acceleration rad/s^2

Thanks :-)

Homework Equations

$\tau = I \alpha$

The Attempt at a Solution

[/B] Example:
t = 12 kg m^2/s^2
I = 3.00 kg m^2

angular acceleration = torque/I = 12 kg m^2/s^2 / 3.00 kg m^2 = 4 units(?) / s^2

 

[gneill]

Yes. Angular acceleration is given in radians per second squared $(rad/s^2)$.

The radian is sort of a "unitless unit" that appears and disappears as required when working with angular quantities. It's based on a ratio of lengths from the unit circle, where an angle is defined via the arclength along the circle divided by the radius length. It serves to distinguish a quantity as being angular in nature.

 

[SDTK]

thank you! :-)

 

[haruspex]

unitless unit

How about "dimensionless unit"?

 

[gneill]

How about "dimensionless unit"?

Sure! That's probably better nomenclature.