Instantaneous Centre of Rotation Trajectory

Classical Mechanics Level 4

A disk placed on a frictionless horizontal plank is rotating with a constant angular velocity $\omega$ about it's central vertical axis in anti-clockwise direction . Now the plank is made to move with a constant acceleration $a$ on a straight path.

If we assume initial location of the centre of disk as origin, direction of motion of the plank in negative $y$ axis of the coordinate system attached with the plank, which equations represent the trajectory of instantaneous centre of rotation of the disk.

y=-\frac{\omega^2x^2}{a}

and

x\leq0

y=-\frac{\omega^2x^2}{2a}

and

x\geq0

y=\frac{\omega^2x^2}{3a}

and

x\geq0

y=\frac{\omega^2x^2}{2a}

and

x\leq0

The path will not be parabolic but a straight line

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Instantaneous Centre of Rotation Trajectory

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