Rotation and translation (of life importance)

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SUMMARY

The discussion focuses on the dynamics of a rotating disc moving along the x-axis, specifically analyzing the instantaneous axis of rotation under two scenarios: (A) the disc moves with a constant velocity while rotating counterclockwise with a constant angular acceleration (β), and (B) the disc accelerates with a constant angular velocity (ω) while starting from rest. The participants clarify that the instantaneous axis of rotation is not trivial, as it always intersects the point of contact between the disc and the ground, which is crucial for understanding the motion dynamics involved.

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FermatPell
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A rotating disc moves in the positive direction of the x axis. Find the equation y(X) describing the position of the instantaneous axis of rotation, if at the initial moment the axis C of the disc was located at the point O after which it moved

(A) with a constant velocity v, while the disc started rotating counterclockwise with a constant angular acceleration (beta) (the initial angular velocity is equal to zero);
(B) with a constant acceleration (omega) (and the zero initial velocity), while the disc rotates counterclockwise with a constant angular velocity (omega)

I don't understand it - if the instantaneous axis of rotation always passes through the point of contact between ground and a disc, isn't it like trivial?

could some1 solve it pls?? its for my gf she will kill me if i don't solve it by the morning. (if she's reading this, go away)
 
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Welcome to PF!

Hi FermatPell! Welcome to PF! :smile:

(have a beta: β and an omega: ω :wink:)
FermatPell said:
… I don't understand it - if the instantaneous axis of rotation always passes through the point of contact between ground and a disc, isn't it like trivial?

I think the disc is flat, not rolling upright. :redface:
 

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