A disc of radius R start at time `t=0` moving along the positive X-axis with linear speed b and angular speed `omega`. Find the x and y-coordinates of the bottommost point at any time t.

Explanation

At time t, the bottommost point will rotate an angle `theta = omegat` with respet to the centre of the disc c. The centre C will travel a distance `s=vt `

In the figure , `PQ=R sin theta = R sin omega t`
and `CQ=R cos theta = R cos omega t`
Coordinates of points P and at time t are,
`x=OM -PQ=vt-R sin omegat`
and `y=CM - CQ = R-R cos omegat`
`:. (x,y)-= (vt-R sin omegat,R-R cos omegat)`