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Units for Precession Rate (Ω)?

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.
 
Last edited:

berkeman

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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?
 
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?
 
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

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

haruspex

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##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.
 

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