# Units for Precession Rate (Ω)?

#### lightlightsup

Homework Statement
The precession rate is given as $Ω = \frac{Mgr}{Iω}$.
Homework Equations
What are the units here?: I'm calculating it as $\frac{1}{rad . s}$.
The precession rate is given as $Ω = \frac{Mgr}{Iω}$.
What are the units here?: I'm calculating it as $\frac{1}{rad . s}$.
Am I supposed to interpret this as revolutions per second, sort of like frequency, and ignore the $rad$?
Also, period is calculated as: $T = \frac{2π}{Ω}$. So, $T$'s units are $\frac{s}{rev}$?
I'm guessing that I don't quite understand yet how $rads$ are ignored in the calculations.
Edit: This refers to gyroscopic precession wherein gravity is the only force causing a torque.

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#### berkeman

Mentor
Homework Statement: The precession rate is given as $Ω = \frac{Mgr}{Iω}$.
Homework Equations: What are the units here?: I'm calculating it as $\frac{1}{rad . s}$.
I get 1/s, which would be the same as the units for ω...

EDIT -- can you show the units you have for the first equation, and what you cancel to get your result?

#### lightlightsup

I get 1/s, which would be the same as the units for ω...
We're ignoring $rads$, I guess? Because they are considered "dimensionless" ratios?

#### lightlightsup

I get 1/s, which would be the same as the units for ω...

EDIT -- can you show the units you have for the first equation, and what you cancel to get your result?
$Ω =\frac{Mgr}{Iω} = \frac{kg . \frac{m}{s^2} . m}{kg.m^2.\frac{rads}{s}} = \frac{1}{rad.s}$
$T = \frac{2π}{Ω} = \frac{\frac{2π}{rad}}{\frac{1}{rad.s}} = s$

I'm sure there is some hole in my logic here somewhere.

#### berkeman

Mentor
Since radians are dimensionless, don't carry them along as units. In that case, you get the correct units for Omega, IMO.

#### haruspex

Homework Helper
Gold Member
2018 Award
$Ω =\frac{Mgr}{Iω} = \frac{kg . \frac{m}{s^2} . m}{kg.m^2.\frac{rads}{s}} = \frac{1}{rad.s}$
$T = \frac{2π}{Ω} = \frac{\frac{2π}{rad}}{\frac{1}{rad.s}} = s$

I'm sure there is some hole in my logic here somewhere.
Over the years there have been numerous attempts to assign a dimension to angles. You can find mine at https://www.physicsforums.com/insights/can-angles-assigned-dimension/
In respect of this thread, the interesting feature is that if we write the dimensionality as Θ then Θ2=1. So 1/rads is the same as rads.