Register to reply

Angular velocity in dimensional analysis

by mightysteve
Tags: analysis, angular, dimensional, velocity
Share this thread:
May15-08, 05:45 AM
P: 11
Hullo was wondering if anyone could help me. In dimensional analysis using then buckingham pi theorum, i'm not sure how to express an angular velocity in terms of basic dimensions (i.e M (mass), L (length), T(time), [tex]\Theta[/tex] (temp).

I know an angular velocity is revs/s or rad/s so its going to be 'whatever radians/ revs are in basic dimensions * T^(-1)

But I'm not sure how to express revs/rads in basic dimensions? Are they just dimensionless?
Phys.Org News Partner Science news on
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100
May15-08, 05:55 AM
rohanprabhu's Avatar
P: 413
Yes. Radian is a dimensionless measure. If there is a circle, and a small part of it's circumference [an arc] subtends an angle [itex]\theta[/itex] radians at the center, then [itex]\theta[/itex] is the ratio of the length of the arc to the radius of that circle. As you can see, a radian is a ratio of two lengths: the arc length and the radius and hence, it is dimensionless as the length dimension of both these quantities cancel each other out.

The 'rad' in 'rad/s' is there to denote that we specifically mean a unit of angular velocity, to seperate it from '/s', which is a unit of frequency. However, angular velocity is also the angular frequency of rotation in a uniform circular motion i.e. it differs from the no. of rotations by a factor of [itex]2\pi[/itex].

As far as revolution is considered, n revolutions just mean [itex]n \times 2\pi[/itex] radians. Even then, revolutions are counted in pure basic numbers. And as you know, there is nothing like a 'kilo numbers' or a 'mega numbers'.. hence revolutions is also a dimensionless unit.
May15-08, 02:21 PM
P: 11
Aah, i see. Thanks very much

Register to reply

Related Discussions
DEs with Dimensional Analysis. Science & Math Textbooks 6
Dimensional analysis Introductory Physics Homework 1
Can someone Help me with Dimensional analysis please Mechanical Engineering 3
Dimensional Analysis Introductory Physics Homework 2
Help on Dimensional Analysis General Math 2