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What is the angular momentum of a figure skater spinning at 3.2 rev/s with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.6 m , a radius of 13 cm , and a mass of 48 kg? (answer for this is 8.16) How much torque is required to slow her to a stop in 4.1 s , assuming she does not move her arms?

What is the angular momentum of a 0.335 kg ball rotating on the end of a thin string in a circle of radius 1.45 m at an angular speed of 10.8 rad/s ?

A merry-go-round with a moment of inertia equal to 1300 kg⋅m2 and a radius of 2.5 m rotates with negligible friction at 1.70 rad/s. A child initially standing still next to the merry-go-round jumps onto the edge of the platform straight toward the axis of rotation, causing the platform to slow to 1.35 rad/s.What is her mass?

billrussell42 · Answer

I = cMR² = ½48•0.13²
ω = 3.2 rev/s x 2π rad/rev = 6.4π rad/s
L = Iω = (24•0.0169)(6.4π) = 8.16 kg•m²/s
α = Δω/Δt = 6.4π / 4.1 = 4.90 rad/s²
τ = αI = 4.9•(24•0.0169) = 1.95 Nm

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angular acceleration in rad/s²
  α = τ/I for constant α
     I = moment of inertia in kg•m²
     τ = torque in N•m
  τ = αI  torque required for that accel.

Angular momentum in kg•m²/s
   L = Iω
   I is moment of inertia in kg•m²
   ω is angular velocity in radians/sec

I is moment of inertia in kg•m²
I = cMR²
    M is mass (kg), R is radius (meters)
    c = 1 for a ring or hollow cylinder
    c = 2/5 solid sphere around a diameter
    c = 7/5 solid sphere around a tangent
    c = ⅔ hollow sphere around a diameter
    c = ½ solid cylinder or disk around its center
    c = 1/4 solid cylinder or disk around a diameter
    c = 1/12 rod around its center, R = length
    c = ⅓ for a rod around its end, R = length
    c = 1 for a point mass M at a distance R from
       the axis of rotation

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