Mass on a slope on a turntable

[Ciaran]

Homework Statement

A wedge with face inclined at an angle theta to the horizontal is fixed on a rotating turntable. A block of mass m rests on the inclined plane and the coefficient of static friction between the block and the wedge is μ. The block is to remain at position R from the centre of the turntable. Show that the acceleration is a=-Rω^(2)r̂ .Find the components of the block's acceleration parallel and vertical to the inclined plane. Finally, find the minimum angular velocity needed to keep the block from sliding down the face of the wedge

Homework Equations

a=-Rω^(2)r̂
3. The Attempt at a Solution
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I'm really not sure how to start this problem- I know I need to use cylindrical coordinates with z constant but apart from that, I'm really stuck. Any help would be much appreciated!

 

[Suraj M]

Start off with a free body diagram, indicate and observe all the forces acting on the body,

 

[BvU]

Hello Ciaran, a belated welcome to PF !

I see you started two other threads earlier on and haven't been house trained wrt the funny habits on PF. Please check the guidelines ! At least this time there is an equation, but your attempt at solution isn't up to snuff.

Nevertheless: A drawing helps, and once you realize the block makes a circular trajectory, things will fall into place very nicely: for such a trajectory the resultant of all forces has to be a centripetal force ma with a as you state in the problem statement. You can draw all applicable forces and add them.