A disc of radius R starts at time t=0 moving along the positive x-axis with linear speed v and angular speed omega. Find the x and y coordinates of the bottom most poitn at any time t.

A disc of radius R starts at time t=0 moving along the positive x-ax

1.	A disc of radius R starts at time t=0 moving along the positive x-axis with linear speed v and angular speed omega. Find the x and y coordinates of the bottom most poitn at any time t.
Answer» <P> Solution : At time `t` the bottommost poit will ROTATE and ANGLE `theta=omegat` with respect to the centre of the disc C. The centre C will travel a distance `s=vt`. In the FIGURE, `PQ=Rsintheta=Rsinomegat` and `CQ=Rcostheta=Rcosomegat` COORDINATES of point P at time t are `x=OM-PQ=vt-Rsinomegat` and `y=CM-PQ=R-Rcosomegat` `therefore(x,y)=(vt-Rsinomegat,R-Rcosomegat)`