Question

A diver comes off a board with arms straight up and legs straight down, giving her a moment of inertia about her rotation axis of 18kg⋅m2. She then tucks into a small ball, decreasing this moment of inertia to 3.6kg⋅m2. While tucked, she makes two complete revolutions in 1.1 s .

Part A

If she hadn't tucked at all, how many revolutions would she have made in the 1.7 s from board to water?

Express your answer using two significant figures.

Answer 1

Part A

From angular momentum conservation,

I1*w1 = I2*w2

here,

I1 = moment of inertia before she tucked = 18 kg*m^2

w1 = angular speed before she tucked = ??

I2 = moment of inertia after she tucked = 3.6 kg*m^2

w2 = angular speed after she tucked = 2 revolution in 1.1 sec.

w2 = 2/1.1 rev/sec.

w2 = 1.82 rev/sec.

So, 18*w1 = 3.6*1.82

w1 = 3.6*1.82/18

w1 = 0.364 rev/sec.

So, in 1.7 sec.

Total revolutions before she hadn't tucked = w1*1.7 = 0.364*1.7

Total revolutions before she hadn't tucked = 0.62 revoltutions

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