Question

P is an 85 kg diver who leaps off the diving board with an angular momentum of 24 kg·m2/s and curls into a ball to rotate (position A). Their radius of gyration when in the ball is 0.3m. P then fully extends into a headfirst diving position (position B) where their radius of gyration is 1.6m. The time from position A to position B occurs in 0.8 seconds. (You do not need to convert radians to meters)

a. What is P’s angular velocity at position A?

b. What is P’s angular velocity at position B?

c. What is P’s angular acceleration between the two positions?

Answer 1

Since there is no external torque about COM, angular momentum about COM remains conserved throughout the motion.

Angular momentum, L = 24 kg-m2/s2

a) Moment of Inertia = mk2 = 85*(0.3)2 = 7.65 kg-m2

Angular velocity = L/I = 24/7.65 = 3.14 rad/s

b) Moment of Inertia = mk2 = 85*(1.6)2 = 217.6 kg-m2

Angular velocity = L/I = 24/217.6 = 0.11 rad/s

c) Angular acceleration = ($\omega$2 - $\omega$ 1)/t = (0.11 - 3.14)/0.8 = -3.79 rad/s2