A small particle of mass m is at rest on a horizontal circular platform that is free to rotate about a vertical axis through its center. The particle is located at a radius r from the axis, as shown in the figure above. The platform begins to rotate with constant angular acceleration α. Because of friction between the particle and the platform, the particle remains at rest with respect to the platform. When the platform has reached angular speed ω, the angle θ between the static frictional for fs and the inward radial direction is given by which of the following?
A. θ = ω2r/g
B. θ = ω2/α
C. θ = α/ω2
D. θ = tan−1(ω2/α)
E. θ = tan−1(α/ω2)
(GR0877 #99)
Solution:f sin θ = Iα = mrα
f cos θ = mω2r
tan θ = α/ω2
Answer: E
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