Understanding Relative Angular Velocity and Acceleration in Rotating Bodies

AI Thread Summary
The discussion focuses on calculating the relative angular velocity and acceleration of two solid bodies rotating about mutually perpendicular axes with constant angular velocities. Participants express confusion about the correct equations to use, particularly questioning the sign in the relative angular velocity equation, ω_{12} = ω_1 - ω_2. There is a need for clarity on treating angular velocities and accelerations as vectors. Additionally, the concept of relative angular acceleration is debated, especially since both bodies are said to rotate with constant angular velocity. Understanding these concepts is essential for solving the problem effectively.
da_vinci
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Homework Statement


Two solid bodies rotate about mutually perpendicular intersecting axes with constant angular velocities \omega_1 and \omega_2. Find the angular velocity and angular accelartion of one body relative to the other.
 
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da_vinci said:

Homework Statement


Two solid bodies rotate about mutually perpendicular intersecting axes with constant angular velocities \omega_1 and \omega_2. Find the angular velocity and angular accelartion of one body relative to the other.
Welcome to PF da_vinci,

It seems that you have missed off two sections of the template...
Homework Help Template said:

Homework Equations



The Attempt at a Solution

You need to show some effort in solving the problem yourself before we can help you :wink:.
 
sorry!
but i didnt know the concept for the relative angular accelaration..
for relative angular velocities, i think we should use this equation
\omega_{12} = \omega_1 - \omega_2
am i right??
can somebody help me with this prob? please?
 
da_vinci said:
sorry!
but i didnt know the concept for the relative angular accelaration..
for relative angular velocities, i think we should use this equation
\omega_{12} = \omega_1 - \omega_2
am i right??
can somebody help me with this prob? please?
Are you sure about that equation, in particular the sign of the equation?
 
i am not too sure of that eqn!
i don't know how to deal with angular velocity and andular accelarations as vectors...please can smone answer this?
 
da_vinci said:
i am not too sure of that eqn!
i don't know how to deal with angular velocity and andular accelarations as vectors...please can smone answer this?
Okay, we'll start from the beginning. We need to determine the angular velocity of one body with respect to the other. Let us arbitrarily chose to determine the angular velocity of the second object with respect to the first.

From our point of view (POV), the first body is rotating about it's axis of rotation wil an angular velocity of \omega_1. However, we need to determine the angular velocity of the axis about the first body from the first body's POV.

Can you do that?
 
The relative angular velocity can be found using analogy to linear ones, am I correct?

Another thing, since the 2 bodies rotate with constant angular velocity, why is there relative angular acceleration?
 

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