# Physical units problem for a DC Motor with viscous friction

• IzitoI
IzitoI
Homework Statement
30*10^-6 N*m*s
Relevant Equations
Hi everyone,

I'm trying to derive DC motor differential equations. I have some doubts:

I have a viscous friction coefficient in terms of N*m*s. Is it possible to express it in terms of N*m*s/rad? And how?

Some exercises show this value in Newton-meter-second and others in Newton-meter-second/rad so I'm a little bit confused.

Thank you Homework Helper
Gold Member
A rad is not really a unit but a dimensionless quantity. It is used to express the measure of an angle as the ratio of the length of an arc ##s## on a circle of radius ##r##, that is ##\theta = s/r##. The angular frequency ##\omega## is given by ##\omega=\frac{d\theta}{dt}## and you see it expressed sometimes as rad/s and sometimes as s-1. To answer your question, 1 s/rad = 1 s.; there is no conversion factor.

• IzitoI and Dr.D
IzitoI
A rad is not really a unit but a dimensionless quantity. It is used to express the measure of an angle as the ratio of the length of an arc ##s## on a circle of radius ##r##, that is ##\theta = s/r##. The angular frequency ##\omega## is given by ##\omega=\frac{d\theta}{dt}## and you see it expressed sometimes as rad/s and sometimes as s-1. To answer your question, 1 s/rad = 1 s.; there is no conversion factor.
I thought was like that but I wasn't sure. Thank you so much 😉

• berkeman
Homework Helper
Gold Member
2022 Award
Hi everyone,

I'm trying to derive DC motor differential equations. I have some doubts:

I have a viscous friction coefficient in terms of N*m*s. Is it possible to express it in terms of N*m*s/rad? And how?

Some exercises show this value in Newton-meter-second and others in Newton-meter-second/rad so I'm a little bit confused.

Thank you There seems to be something wrong with one of your units.
For viscous friction coefficient, you can have Ns/m for linear or Nms/rad for rotational.
See e.g. https://lpsa.swarthmore.edu/Systems/MechRotating/RotMechSysElem.html
There is no Nms.

More generally, there have been many attempts to ascribe dimension to rotation, and it can be done, but it turns out to be "imaginary" in the sense that although radian has this new dimension radian2 is dimensionless.