Understanding Relative Angular Velocity and Acceleration in Rotating Bodies

[da_vinci]

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.

 

[Hootenanny]

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,

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Homework Equations

The Attempt at a Solution

You need to show some effort in solving the problem yourself before we can help you .

 

[da_vinci]

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?

 

[Hootenanny]

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?

 

[da_vinci]

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?

 

[Hootenanny]

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?

 

[psychicist]

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?