A woman weighing 620 N does a handstand dive from the 10 m diving platform. Afte

Question

A woman weighing 620 N does a handstand dive from the 10 m diving platform. After she leaves the platform (position A), she has an angular momentum of 85 kg m2/s and a radius of gyration of 0.75 m. What is her angular velocity in radians per second and in revolutions per second at position A? (Hint: 2? radians equals 1 revolution.) If she assumes a tuck position, reducing her radius of gyration to 0.35 m in position B, what will her angular velocity be in rad/s and rev/s?

Angular velocity in radians per second at A______________

Angular velocity in revolutions per second at A ______________

Angular velocity in radians per second at B ______________

Angular velocity in revolutions per second at B ______________

Explanation / Answer

here,

weight of woman , w = 620 N

mass , m = w/g

m = 63.27 kg

angular momentum , L = 85 kg.m^2/s

radius of gyration , ra = 0.75 m

rb = 0.35 m

at A

Ia * wa = L

m * ra^2 * wa = L

63.27 * 0.75^2 * wa = 85

wa = 2.39 rad/s

the angular velocity at A is 2.39 rad/s and 0.38 rev/s

using conservation of angular momentum

L = Ia * wa = Ib * wb

85 = m * rb^2 * wb

85 = 63.29 * 0.35^2 * wb

wb = 10.96 rad/s

the angular velocity at B is 10.96 rad/s

the velocity in rev/s is 1.75 rev/s

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