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A rotating disc moves in the positive di...


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 of 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 `alpha`. the initial angular velocity is equal to zero.

Text Solution

Verified by Experts

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)
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