Units for Precession Rate (Ω)?

In summary, the precession rate is given in terms of revolutions per second (rad/s), period is in terms of seconds (s), and T is in terms of radians (rad).
  • #1
lightlightsup
95
9
Homework Statement
The precession rate is given as ##Ω = \frac{Mgr}{Iω}##.
Relevant 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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  • #2
lightlightsup said:
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?
 
  • #3
berkeman said:
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?
 
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  • #4
berkeman said:
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.
 
  • #5
Since radians are dimensionless, don't carry them along as units. In that case, you get the correct units for Omega, IMO.
 
  • #6
lightlightsup said:
##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.
 

What is the unit for precession rate (Ω)?

The unit for precession rate is radians per unit of time, commonly expressed as radians per year (rad/yr) or radians per century (rad/cent).

How is precession rate measured?

Precession rate is typically measured using astronomical observations, such as tracking the motion of stars or planets over time. It can also be calculated using mathematical models based on the known forces acting on a rotating object.

What factors affect the precession rate of an object?

The precession rate of an object can be influenced by several factors, including the object's shape, mass distribution, and external forces such as gravitational pulls from nearby objects. It can also be affected by the object's rotation speed and tilt.

Can precession rate change over time?

Yes, precession rate can change over time due to various factors, such as changes in the object's rotation or external forces acting on it. It can also be affected by long-term changes in the Earth's orbit or other astronomical events.

Why is precession rate important in scientific research?

Precession rate is important in scientific research because it can provide valuable information about the motion and behavior of objects in space. It is also a key factor in understanding phenomena such as the Earth's axial tilt and the precession of the equinoxes.

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