My Math Forum  

Go Back   My Math Forum > Science Forums > Physics

Physics Physics Forum


Thanks Tree2Thanks
  • 1 Post By fysmat
  • 1 Post By fysmat
Reply
 
LinkBack Thread Tools Display Modes
August 23rd, 2014, 03:35 AM   #1
Senior Member
 
Joined: Jan 2013
From: Italy

Posts: 154
Thanks: 7

Simple exercise on determine some dimensions.

Hi,

I have this exercise about determine the dimensions in a equation. But I have some problem during the way. This is the exercise:

Given that $\displaystyle v = A \cdot \omega \cdot sin(\omega \cdot t )$, where $\displaystyle v$ has dimensions of speed and $\displaystyle t$ is a time, determine the dimensions of $\displaystyle \omega$ and $\displaystyle A$.


I have tried this, using SI units, but without success...:
$\displaystyle \frac{m}{s} = A \cdot \omega \cdot sin(\omega \cdot sec)$

Please, can you give me a help on how to proceed?
Many thanks!
beesee is offline  
 
August 23rd, 2014, 05:53 AM   #2
Senior Member
 
fysmat's Avatar
 
Joined: Dec 2013
From: some subspace

Posts: 212
Thanks: 72

Math Focus: real analysis, vector analysis, numerical analysis, discrete mathematics
Dimension of $\displaystyle \omega \cdot t$ must be one, because the argument of the sine function must be dimensionless. Thus the unit of $\displaystyle \omega$ is $\displaystyle \frac{1}{\textrm{s}}$.

The sine function is also dimensionless, so what is left, is

$\displaystyle \frac{\textrm{m}}{\textrm{s}} = \left[ A \right] \cdot \frac{1}{\textrm{s}}$.

Hence the unit of $\displaystyle A$ is m.
Thanks from beesee
fysmat is offline  
August 23rd, 2014, 09:20 AM   #3
Senior Member
 
Joined: Jan 2013
From: Italy

Posts: 154
Thanks: 7

ok I understand, but, why in the solution of the exercise I have dimensions of $\displaystyle \omega$ as $\displaystyle \frac{rad}{s}$ ?
beesee is offline  
August 23rd, 2014, 10:48 AM   #4
Senior Member
 
fysmat's Avatar
 
Joined: Dec 2013
From: some subspace

Posts: 212
Thanks: 72

Math Focus: real analysis, vector analysis, numerical analysis, discrete mathematics
Radian is an angle unit. If you take a look how it is defined, you can see that it is actually dimensionless. The unit, radian, is put there mostly because of clarity. Or, they may have thought that the argument of the sine function is explicitly in radians (to avoid confusion, maybe(?)), and thus they've put the unit there.
Thanks from beesee
fysmat is offline  
August 23rd, 2014, 02:10 PM   #5
Senior Member
 
Joined: Jan 2013
From: Italy

Posts: 154
Thanks: 7

ok I understand!
Quote:
Radian is an angle unit. If you take a look how it is defined, you can see that it is actually dimensionless.
yes as here: Radian - Dimensional analysis
Quote:
they may have thought that the argument of the sine function is explicitly in radians
here in the exercise in can't read anything about the use of radians however.

I could recap all as the following:
Sine must be dimensionless, so giving to omega the rad unit and to t the sec unit (because in the exercise it is stated that t is time, and his unit, in SI, MUST BE sec.), to obtain sine dimentionless we must attribute to omega the unit rad/sec instead of rad.

So we could think like this:





So and

or not?
beesee is offline  
Reply

  My Math Forum > Science Forums > Physics

Tags
determine, dimensions, exercise, simple



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
determine the dimensions of the box with maximum volume shawen Calculus 1 July 25th, 2014 01:49 AM
A simple exercise in the number field Simple Minded Real Analysis 1 December 12th, 2013 08:57 AM
Need simple help to determine angles in right triangle? MathNoobGuy Algebra 4 March 1st, 2012 10:32 AM
Dimensions MattJ81 New Users 3 July 27th, 2011 11:40 PM
Simple trig in 3 dimensions (2 functions) deianthropus Algebra 2 March 31st, 2010 02:56 PM





Copyright © 2018 My Math Forum. All rights reserved.