A hollow cylinder of radius 1 m rotates with angular velocity:
ω = 10 rad/s
A block of mass M is pressed against the inner wall of the cylinder.
Find the minimum coefficient of friction required so that the block remains at rest relative to the cylinder.
As the cylinder rotates, the block moves in a circular path.
The normal reaction provides the required centripetal force.
Therefore:
N = mω²r
Substituting:
N = m × 10² × 1
N = 100m
The block tends to slide downward due to gravity.
To prevent slipping:
Maximum friction = Weight
μN = mg
μ(100m) = mg
μ = g/100
Taking:
g = 9.8 m/s²
μ = 9.8/100
μ = 0.098
≈ 0.10
Final Answer
Minimum coefficient of friction = 0.098 ≈ 0.10