1. The total-body angular momentum of a diver changes from zero to some signific

Question

1. The total-body angular momentum of a diver changes from zero to some significant value (positive or negative depending on the type of dive) during the takeoff phase. Miller and Munro (1985) reported that Greg Louganis had an angular momentum at takeoff of -65 kg·m2 /s in the forward 3.5-somersault dive performed in the closed pike position, an angular momentum of 50 kg·m2 /s in the reverse 2.5-somersault dive in the open pike position, and an angular momentum of -19 kg·m2 /s in a straight forward dive (layout).

a. What does a negative angular momentum indicate? Why does the magnitude of the angular momentum differ for the three dives?

b. Use the moment of inertia values in the following table to calculate the average angular velocity for each of the three dives.

12.55

c. The duration of the takeoff phase was 0.42 s, 0.44 s, and 0.39 s, respectively. Calculate the angular impulse and the average torque about the center of mass for each of the dives.

Postion Moment of Inertia (kg m^2) layout

12.55

open pike (arms out to side) 8.38 closed pike (fingers touching toes) 8.65 tuck 4.07

Explanation / Answer

a) it indicates that the direction of momentum is opposite to the direction of observation. obviously the values will be different for diving in different manners.

b) as angular velocity = angular momentum/ moment of inertia.

so for layout ,, w = -19/12.55 = -1.5139 rad/sec.

open pike,, w =50/8.38 = 5.967 rad/sec.

closed pike,, w = -65/8.65 = -7.514 rad/sec.

c)

angular impulse is same as the angular momentum values.

also average torque = angular momentum / time

layout torque, t = 19.55/0.39 = 50.13 Nm

open peak , t = 50/0.44 = 113.64 Nm

closed peak t = 65/0.42 = 154.76 Nm

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