During last year’s diving competition, the divers always pull their
limbs in and curl up their bodies when they do flips. Just before
entering the water, they fully extend their limbs to enter straight down
as shown.
Explain the effect of both actions on their angular velocities and
kinetic energy (support your answer with working). Also explain the
effect on their angular momentum.

The divers pull in their limbs and curl up their bodies because doing so decreases their moment of inertia and increases their angular velocity

Explanation:

The conservation of angular momentum states that in a rotational system, the initial angular momentum is equal to the final angular momentum if no torque acts on it.

Angular momentum is equal to the product of the moment of inertia about its axis and the angular velocity

Angular momentum = Iω

where I = moment of inertial = mass x

I = m

angular momentum = mω

since angular momentum is constant, one can see that decreasing the radius of rotation about the body by curling in the limb will cause the moment of inertia to decrease and the angular velocity to increase.

NB: mass of the body is constant.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft