[10 Points) The two disks shown below are connected by a belt which does not slip as disks rotate. Disk A has a radius
of 0.50 m and a mass of 2.00 kg, while disk B has a radius of 0.75 m and unknown mass. For the two disks have the
same angular momentum, what must be the mass of disk B? Assume that disk A is being rotated with an angular speed
of 1.50 rev/s and treat the disks as uniform cylinders. (Hint: When two disks are connected by a belt that does not slip,
the linear speeds at the rim of each disk are equal.)


  1. Answer:

    m₂ = 1.33 kg


    1.50 rev/s = 3π rad/s

    I₁ = ½(2.00)(0.50²) = 0.25 kg•m²

    L₁ = I₁ω₁ = 0.25(3π) = .075π kg•m²/s

    ω₂ = ω₁R₁/R₂ = 3π(0.5/0.75) = 2π rad/s

    I₂ = L₂/ω₂ = 0.75π/2π = 0.375 kg•m²

    I₂ = ½m₂R₂²

    m₂ = 2I₂/R₂² = 2(0.375) / 0.75² = 1.33 kg

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