Rigid body dynamics: falling stick

AI Thread Summary
The discussion focuses on determining whether a falling stick will stick or slip on a table, given its mass, length, and friction coefficients. The user attempts to analyze the forces acting on the stick using a free body diagram (FBD) but struggles with identifying the forces in the x-direction that would cause slipping. They derive an angular acceleration equation based on gravitational force and the angle of the stick, but seek clarification on the translational acceleration and the role of kinetic friction. The conversation highlights the complexities of rigid body dynamics in relation to friction and motion. The user is looking for guidance on their calculations and the conditions for slipping versus sticking.
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Homework Statement


A stick of length L and mass m is falling on a table with kinetic friction uK and static friction uS. Find the equation that determines whether the rod will stick or slip.

If m = 10kg and L = 100cm, uS = 0.8, uK = 0.7 and initial theta = 30 degrees find the initial accel for stick and slip.

Homework Equations


Irod = (1/3)mL^2
M= r x F

The Attempt at a Solution


I'm so stuck.

I made an FBD but as far as I can see, there are no forces in the X-direction, so what exactly makes the thing slip?
 
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From my FBD:

Iα = -mg(L/2)Sinθ

then α = -(3/2L)gsinθ

so far so good?
 
By which the translational x-acceleration of the rod must be (taking positive x to the left):

Ax= -αRSinθ - uK*N / m

correct?
 
Nobody?
 
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