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Homework Help
Introductory Physics Homework Help
Angular velocity and acceleration
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[QUOTE="Nikstykal, post: 5483101, member: 584563"] [h2]Homework Statement [/h2] Small mass sits on a circular revolving table, 200 mm from center. It is given a constant angular acceleration of 2 rad/s. The static coefficient of friction is 0.2. At what angular velocity will the mass start to slip? [ATTACH=full]188058[/ATTACH] [h2]Homework Equations[/h2] a[SUB]r[/SUB]=v[SUP]2[/SUP]/r a[SUB]r[/SUB]=r''-rθ'[SUP]2[/SUP] a[SUB]θ[/SUB]=rθ''+2r'θ' ΣF[SUB]i[/SUB]=ma[SUB]i[/SUB] F[SUB]f,max[/SUB]=μN [h2]The Attempt at a Solution[/h2] I first set up a free body diagram with w[SUB]mass[/SUB] pointing downwards, F[SUB]f[/SUB] pointing left, normal pointing upwards, with a[SUB]r[/SUB] vector pointing to the right. Since the distance is unchanging, r = 0.2m, r'=0, r''=0. θ''=2rad/s, θ'=2t rad/s + c, θ=t[SUP]2[/SUP]+ct+d ΣF[SUB]z[/SUB]=ma[SUB]z[/SUB]=N-mg, since a[SUB]z[/SUB]=0, N=mg ΣF[SUB]r[/SUB]=ma[SUB]r[/SUB]=m(r''-rθ'[SUP]2[/SUP])=-F[SUB]f[/SUB] Combining: m(r''-rθ'[SUP]2[/SUP])=-μmg Simplifying: -rθ'[SUP]2[/SUP]=-μg θ' = ω = √(μg/r) θ' = √(0.2⋅(9.81m/s[SUP]2[/SUP])/0.2m) = 3.13 rad/s Does this look correct? I never used the given angular acceleration so I feel like I missed something. Thank you. [/QUOTE]
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Introductory Physics Homework Help
Angular velocity and acceleration
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