A woman whose mass is 54.7 kg stands at the rim of a horizontal turntable which

Question

A woman whose mass is 54.7 kg stands at the rim of a horizontal turntable which has a moment of inertia of 338 kg m* about the axis of rotation and a radius of 2.26 m. The system is initially at rest and the turntable is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim in a clockwise direction (viewed from above) at a constant speed of 0.873 m/s relative to the ground What will the motion of the turntable be, relative to the ground 1. rotating clockwise 2. rotating counterclockwise 3. at rest, nonrotating Question 21, chap 111, sect 10. part 2 of 3 10 points What is its angular speed? Answer in units of rad/s. Question 22, chap 111, sect 10. part 3 of 3 10 points How much work does the woman do to set the system into motion? Answer in units of J

Explanation / Answer

a) Moment of Inertia = Mr^2 = (2.26^2) M = 338

M = 338/5.108 = 66.18 kg

(54.7 * 0.873) + (66.18 * v) = 0

This assumes that 0.873 is the positive direction or counterclockwise

v = (-54.7 * 0.873) / 66.18 = -0.72 m/s

v = wr = 2.26 w = -0.72

w = -0.72 / 2.26 = 0.32 rad/s clockwise

b) Gain in KE for the woman = mv^2/2 = 54.7 * 0.873^2 / 2 = 20.84 J

Gain in KE for the turntable = 66.18 * 0.72^2 / 2 = 17.15 J

Total work done = 20.84 + 17.15 = 38 J

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