Adiver comes off a board with arms straight up and legs straight down, giving her a moment of
inertia about her rotation axis of 18 kg. m2
. she then tucks into a small ball, decreasing this
moment of inertia to 3.6 kg. m2
. while tucked, she makes two complete revolutions in 1.0 s. if
she hadn’t tucked at all, how many revolutions would she have made in the 1.5 s from board to
water?

0.19 rev

Explanation:

We can solve the problem by using the law of conservation of angular momentum. In fact, if we assume there are no external torques acting on the diver, the angular momentum must be conserved:

where

L is the angular momentum

I is the moment of inertia

is the angular velocity

- When the diver is tucked,

is her moment of inertia

She makes 2 revolutions (so, ) in t = 1.0 s, so her angular velocity is

So her angular momentum is

- When the diver is not tucked,

The angular momentum is conserved, so

the moment of inertia is

So the angular velocity is

So in a time of t = 1.5 s, the angular displacement is

Converting into revolutions,

explanation:

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