Ansh asked in Science & MathematicsPhysics · 8 months ago

Physics question help; picture attached?

https://imgur.com/a/VvOzTlH

Through what angle does the disk rotate

while sliding before it begins to roll without slipping. g = 9.8m/s^2. Answer in units of rev.

1 Answer

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  • NCS
    Lv 7
    8 months ago
    Best Answer

    Relevant equations:

    torque τ = friction force * radius = f*r = µmgr

    so τ = 0.03 * 6kg * 9.8m/s² * 0.50m = 0.882 N·m

    also

    τ = I*α

    so

    0.882 N·m = (6/7)mr² * π = (6/7) * 6kg * (0.50m)² * α

    means that

    α = 0.686 rad/s²

    we are interested in the point at which the linear velocity is equal to the angular velocity * the radius:

    v = (ω₀ - αt)*r

    v = a*t = µg*t = 0.03 * 9.8m/s² * t = 0.294m/s² * t

    so substituting for v and ω₀ and α and r above gives

    0.294t = (3 - 0.686t)*0.5

    solves to

    t = 2.355 s

    then the angle rotated through while it gets traction is

    Θ = ω₀*t - ½*α*t² = 3rad/s*2.355s - ½*0.686rad/s²*(2.355s)²

    Θ = 5.1 rads = 296º

    barring computational error

    Hope this helps!

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