A rotating disc moves in the positive direction of `x`-axis as shown. 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 origin after which
a. it moved with constant acceleration a (initial velocity zero) while the disc rotating anticlockwise with constant angular velocity `omega`. b. it moved with constant velocity `v` while the disc started rotating anticlockwise with a constant angular acceleration a (with initial angular velocity zero).

Explanation

Let the coordinate of instantaneous centre of rotation at any time `t` be (x,y).
Now, `v=omegay`
`sqrt(2ax)=omegay`
`:. y^2=((2a)/omega^(2))x(parabola)`
b. `v=omegay`
`v=(ax y)/v`
`:. xy=(v^(2))/alpha=` constant (rectangular hyperbola)