Question

A diver off the high board imparts an initial rotation with their body fully extended before going into a tuck and executing three back somersaults before hitting the water. If their moment of inertia before the tuck is 16.9kg·m2 and after the tuck during the somersaults is 4.2kg·m2, what rotation rate must the diver impart to their body directly off the board and before the tuck if they take 1.4 s to execute the somersaults before hitting the water?

a) 2.0rad/s
b) 1.5rad/s
c) 3.0rad/s
d) 4.5rad/s

Answer 1

The rotation rate that the diver must impart to their body directly off the board and before the tuck is approximately 0.35 rad/s.

Step-by-step explanation:

The rotation rate that the diver must impart to their body directly off the board and before the tuck can be calculated using the conservation of angular momentum equation. According to the equation, the initial moment of inertia multiplied by the initial rotation rate should be equal to the final moment of inertia multiplied by the final rotation rate. Assuming the initial rotation rate is 'x', the equation becomes:

16.9 kg·m² * x = 4.2 kg·m² * 1.4 rad/s

Solving for 'x' gives us:

x = (4.2 kg·m² * 1.4 rad/s) / 16.9 kg·m²

x ≈ 0.35 rad/s

Therefore, the rotation rate that the diver must impart to their body directly off the board and before the tuck is approximately 0.35 rad/s.