Simulink DC motor model units confusion

Hi there

In the DC motor simulink model in the following link, there are two versions one for simulink and the other for Simscape

http://ctms.engin.umich.edu/CTMS/index.php?example=MotorSpeed&section=SimulinkModeling

My problem is with the units of motor viscous friction constant and angular velocity.

It is N.m.s in simulink version and N.m/rad/sec in the simscape version. However it uses the same equation

If d theta/dt in (rad/sec) so, b should be in (N.m.rad/sec), am i right or what ??

By the way dividing Torque/moment of inertia will give us acceleration in (1/sec^2) how it will be rad/sec after integration ?

[Andy L]

https://answers.yahoo.com/question/index?qid=20081116183435AAFRtYF for your last question

[ameen]

Thank you Andy for your reply but it doesn't answer my question because its answer was: integration of (1/s^2) = (-1/sec). So, where the rad/sec comes from ??

Answer 1

[A Jenkins]

Radians are a dimensionless quantity, since they are calculated as arc length/radius (whatever units those are measured in would cancel). Therefore having radians as a unit can be cancelled out of an equation. Leaving them in does not change the math, but simply clarifies that the angles should be measured in radians and not degrees.

Example:

rad/sec = (arc length / radius) / sec = (meters / meters) / sec = 1/sec

[ameen]

Thank you for your reply however there is a (2 pi) difference between 1/sec and rad/sec.

Regarding the DC simulink model, Should (d theta/dt) in rad/sec or (1/sec) and based on this should the damping coefficient unit to be (N.m.s) or N*m/(rad/s) ??