Question

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.

Answer 1

the angular speed of the person increases, being able to make more turns and faster.

K₂ = K₁ I₁ / I₂

Step-by-step explanation:

When the divers are turning the system is isolated, so all the forces are internal and therefore also the torque, therefore the angular momentum is conserved

initial, joint when starting to turn

L₀ = I₁ w₁

final. When you shrink your arms and legs

Lf = I₂ w₂

L₀ = Lf

I₁ w₁ = I₂ w₂

when you shrink your arms and legs the distance to the turning point decreases and since the moment of inertia depends on the distance squared, the moment of inertia also decreases

I₂ <I₁

w₂ = I₁ / I₂ w₁

therefore the angular speed of the person increases, being able to make more turns and faster.

When it goes into the water it straightens the arm and leg, so the moment of inertia increases

I₁> I₂

w₁ = I₂ / I₁ w₂

therefore we see that the angular velocity decreases, therefore the person trains the water like a stone and can go deeper faster.

In both cases the kinetic energy is

K = ½ I w²

the initial kinetic energy is

K₁ = ½ I₁ w₁²

the final kinetic energy is

K₂ = ½ I₂ w₂²

we substitute

K₂ = ½ I₂ (I₁ / I₂ w1² 2

K₂ = ½ I₁² / I₂ w₁² = (½ I₁ w₁²) I₁ / I₂

K₂ = K₁ I₁ / I₂

therefore we see that the kinetic energy increases by factor I₁/I₂