At the 1984 Olympics, the great diver Greg Louganis won one of his 10 gold medal

Question

At the 1984 Olympics, the great diver Greg Louganis won one of his 10 gold medals for the reverse 3? somersault tuck dive. In the dive, Louganis began his 3 turns with his body tucked in at a maximum height of approximately 2.0 m above the platform, which itself was 10.0 m above the water. He spun uniformly 3 times and straightened out his body just as he reached the water. A reasonable approximation is to model the diver as a thin uniform rod 2.0 m long when he is stretched out and as a uniform solid cylinder of diameter 0.75 m when he is tucked in.

Explanation / Answer

The angular velocity will be:

w = C/T

C = 2 pi x 3.5 = 21.98

T = sqrt (2H/g) ; H = 10 + 2 = 12 m

T = sqrt (2 x 12/9.81) = 1.56

w = 21.98/1.56 = 14.1 rad/s

Intial and final moment of inertia is:

I1 = 1/2 M R^2 = 0.5 x 80 x 0.375^2 = 5.625 kg-m^2

I2 = 1/12 M L^2 = 1/12 x 80 x 2^2 = 26.67 kg-m^2

from conservation of angular momentum

Li = Lf

I1w1 = I2w2

w2 = 5.625 x 14.1/26.67 = 2.97

Intial KE = 1/2 I1 w1^2

KEi = 0.5 x 5.625 x 14.1^2 = 559.15 J

KEf = 0.5 x 26.67 x 1.96^2 = 51.23 J

delta KE = 559.15 - 51.23 = 507.92 J

Hence, KE = -507.92 J

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