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12 March, 00:44

This set of questions uses an interesting formula. A torque applied for a certain time causes a change in angular momentum. Δt=ΔL. It is just like the impulse momentum theorem which says that a force applied for a certain time causes a change in momentum, FΔt=Δp. Lindsey is on the merry-go-round again. Her mass is 33.0kg. The merry-go-round has a mass of 78.0kg and a radius of 2.20m. Lindsey is standing 0.150m from the center and has an initial angular velocity of 3.45radsec. Her older brother Mike applies a force of 200N tangent to the outer edge for 0.800s causing the merry-go-round to spin faster. What was the initial angular momentum before Mike pushed, in kgm2s?

2nd Question: How much torque did Mike apply?

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  1. 12 March, 03:11
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    a. 653.79 kgm²/s b. 440 Nm

    Explanation:

    a. The initial angular momentum

    The initial angular momentum L of the boy and merry-go-round is

    L = Iω where I = moment of inertia of merry-go-round + moment of inertia of Lindsey about merry-go-round and ω = initial angular velocity = 3.45 rad/s

    moment of inertia of merry-go-round I₁ = 1/2MR² where M = mass of merry-go-round = 78 kg and R = radius of merry-go-round = 2.20 m

    I₁ = 1/2MR² = 1/2 * 78 kg * (2.20 m) ² = 188.76 kgm²

    moment of inertia of Lindsey about merry-go-round I₂ = mh² where m = mass of boy = 33.0 kg and h = distance of Lindsey from center of merry-go-round = 0.150 m

    I₂ = mh² = 33.0 kg * (0.150 m) ² = 0.743 kgm²

    I = I₁ + I₂ = 188.76 kgm² + 0.743 kgm² = 189.503 kgm²

    So, L = Iω = 189.503 kgm² * 3.45 rad/s = 653.79 kgm²/s

    b. How much torque does Mike apply?

    Since torque τ = FRsinθ where F = force = 200 N, R = radius of merry-go-round = 2.20 m and θ = 90° (since the force is applied tangentially to the merry-go-round)

    τ = FRcosθ

    = 200 N * 2.20 m * sin90°

    = 440 Nm
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