How do I visualise the equations from observation of a spinning wheel

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shivaniits
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From this figure we could see the axis of rotation of wheel is y-axis and it's translational motion is along x-axis
How would I describe it's horizontal motion in terms of rotational motion
The wheel is spinning and also moving horizontally along x-axis
w being the angular frequency
 
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I meant to say How do we describe the equations of motion of such spinning wheel
Thanks
 
The usual way is to write one equation for the motion of the center of mass and another equation for the rotation around the center of mass.
 
Alright I will try those and post them for verification
Thanks :)