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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 centre c of the disc was located at the point O after which it moved with constant velocity v while the disc started rotating counterclockwise with a constant angular acceleration $α$ . The initial angular velocity is equal to zero.

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(3)xy = $\frac{v^{2}}{α}$

(1) $y = \frac{v^{2}}{α} x$

(4) None of above

(2) $y = \frac{v^{2}}{α} x^{2}$

answer is C.

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Detailed Solution

$t = \frac{x}{v}$ and $ω = αt = \frac{αx}{v}$

The position of I C will be at a distance

$y = \frac{v}{ω} or y = \frac{v}{\frac{αx}{v}}$

$y = \frac{v^{2}}{αx} or xy = \frac{v^{2}}{α} = constant$

This is the desired x-y equation. This equation represents a rectangular hyperbola.

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