A 0.80-kg bead slides on a wire bent into a circle of radius 0.40 m.You pluck the bead with a force tangent to the circle.What force is needed to give the bead an angular acceleration of 3.0 rad/s²? A)4.40 N B)0.71 N C)0.83 N D)0.96 N E)1.2 N

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Quizplus · Accepted Answer

The torque required for angular acceleration is τ = Iα, where I is the moment of inertia and α is the angular acceleration. For a point mass, I = mr². Thus, τ = mr²α. The force needed is F = τ/r = mrα. Substituting m = 0.80 kg, r = 0.40 m, and α = 3.0 rad/s² gives F = 0.80 * 0.40 * 3.0 = 0.96 N.

A 080-Kg Bead Slides on a Wire Bent into a Circle