Circular Motion Problems: Maximum Angular Speed and Slip Calculation

[Sciphi]

A block of mass m is kept on a horizontal ruler.Friction coefficient is k.The ruler is kept at one end and the block is at a distance L from the fixed end.The ruler is roated about the fixed end in the horizontal plane thru the fixed end.(a)what can the maximum angular speed be for which the block does not slip.(b) If the angular speed of the ruler is uniformly increased from zero at an angular acceleration a at what angular speed will the block slip..

I've already figured out part (a) please give me some hints as how to work out part (b)

 

[ceptimus]

You have two forces on the block now. One is the centripetal force which you already worked out. The other is at right angles, accelerating the block (increasing its angular speed). You have to add these two vectors to get the total force.

As the forces are at right angles, you can use Pythagoras to add them.

Total force = sqrt((centripetal force)^2 + (tangential force)^2)

 

[andrevdh]

As the angular speed increases the frictional force will also increase to provide the centipetal force, but the static friction can only increase up to a certain limiting value! Which will limit the maximum angular speed before it starts to slip.