A disc rolls without slipping on a horizontal surface such that its velocity of center of the mass is `v`. Find the velocity of points `A`,`B`,`C` and `D`.

Explanation

If a body rolls without slipping, the velocity of a point of a body is resultant of two velocities, one due to translation of body and another due to rotation of body about its center of mass.

Point `A` :
`v_(A)=sqrt2v, theta=45^(@)`
Point `B` :
`v_(B)=sqrt(v^(2)+v^(2)+2vxxvcostheta30^(@))`
`=sqrt(2v^(2)+sqrt3v^(2))=ysqrt(2+sqrt3)`
Point `C` :
`v_(C)=sqrt(v^(2)+((v)/(2))^(2))=(sqrt5v)/(2)`
Point `D` :
`v_(D)=sqrt(v^(2)+((v)/(3))^(2)+2xxvxx(v)/(3)cos120^(@))`
`=sqrt(v^(2)+((v^(2))/(9))-(v^(2))/(3))=(sqrt7v)/(3)`