Question

A body Is placed on a turntable. The friction coefficient between the body and the table is `mu`.
(a) If turntable rotates at constant angular speed `omega`, find the maximum value of `omega` for which the block will not slip.
(b) if the angular speed is increased uniformly from rest with an angular acceleration `alpha`, at what speed will the block slip?

Answer 1

(a) `f=momega^(2)r`
`f_(max)=muN=mumg`
For no slipping, we have
`momega^(2)rlemumg`
`omegalesqrt((mug)/(r ))`
`omega_(max)=sqrt((mug)/(r ))` (b) This is the case of non-uniform circular motion (As shown in the previous problem), here`a_(t)=ralpha`.
`sqrt((momega^(2)r)^(2)+(m r alpha)^(2))lemumg`
`omegale[((mug)^(2)-(ralpha)^(2))/(r^(2))]^(1//4)`
`omega_(max)=[((mug)/(r ))^(2)-alpha^(2)]^(1//4)`