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A conical wheel is rolling (without slipping) around a fixed axis OZ as shown in the figure. The velocity of point C is v_{c}= at.

The direction of the velocity of C is shown by a cross i.e. along negative x-axis.

We have to find the angular velocity, angular acceleration of the wheel and also the velocity and acceleration of point B.

Now, using the Euler's equation, we can write it as

v_{a}= v_{o}+ ω x OA

As rolling is without slipping, v_{a}is 0 and v_{o}is also 0.

So, I got ω x OA = 0. That means that ω ιι OA. That means ω_{x}and ω_{z }are both zero.

Now, I used the Euler equation for point O and C,

v_{c}= v_{o}+ ω_{y}X OC.

Solving this, I got ω_{y}= -2at/r√3

That means ω = (0) i + (-2at/r√3 ) j + (0) k

So, I got the angular velocity vector along negative y axis. I am confused that is this the angular velocity of the wheel with respect to its own axis, or the angular velocity of the entire wheel with respect the the central axis OZ or the net angular velocity considering the angular velocity around its own axis + angular velocity around the central axis OZ?

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# Homework Help: Angular velocity of a wheel rolling around a fixed axis

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