Applications involving Friction - - Rigid Bodies in Translation and Rotation

Case 1: Assume friction is sufficient to prevent sliding and the disk starts from rest.

Step 2	Write equations of motion ΣF = m a and ΣM = Ic α
Step 3	Use kinematics ac = ap + ac/P|n + ac/P|t to show acx = ˗ rα
Step 4	Solve for F and for N
Step 5	Calculate Fmax = μN
Test	If |F| > |Fmax| , then friction is insufficient to prevent sliding and sliding occurs You then need to consider cases where disk rolls and slides.

Here F is the frictional force, N is the normal force, and μ is the coefficient of friction.

Case 2: Assume sliding occurs in the + x -direction and the disk starts from rest.

Use the Free Body Diagram shown above.

Step 2	Assume Fmax = μN since sliding is presumed to occur.
Step 3	Write equations of motion ΣF = m a and ΣM = Ic α
Step 4	Solve for acx and for F.
Step 5	Use kinematics to calculate aPx , the x-component of the acceleration of the contact point of the disk with the mating surface aP = ac + aP/C|n + aP/C|t
Test	If F is opposite aPx, then done and assumption was correct. Else test sliding in other direction. Need to change FBD since direction of the friction force changes.

Case 3: Assume sliding occurs in the ˗ x -direction and the disk starts from rest.

Repeat steps as in Case 2 using the revised FBD.

Click here for an example.

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