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Determine couple - Homogeneous cylinder:
Homogeneous cylinder having weight W rests on horizontal floor in contact with wall (Figure given below). If the coefficient of friction for the all contact surfaces be µ, determine couple M acting on cylinder, which will begin counter clockwise rotation.
Sol.: ∑H = 0 R1 - µR2 = 0
R1 = µR2 ...(i)
∑V = 0 => R2 + µR1 = W ...(ii)
Putting value of R1 in equation (ii), we get
R2 + µ2R2 = W
R2 = W/(1 + µ2) ...(ii)
Putting value of R2 in equation (i), we get
R1 = µW/(1 + µ2) ...(iv)
Taking the moment about O, we get
MO = µR1r + µR2r
= µr{R1 + R2}
= µr{(µW/(1 + µ2)) + (W/(1 + µ2))} = µrW{(1 + µ)/(1 + µ2)}
MO = µrW(1 + µ)/(1 + µ2) .......ANS
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