Question

A 140-lb diver performs a 1 ½ flip off a diving board. While spinning 1220deg/s, the diver has a radius of gyration of 0.3m. What is the angular momentum at this point?

Please show all work and steps, including conversions

Answer 1

Angular momentum is the quantity of a rotation of a body which is the product of moment of inertia and its angular velocity.

i.e, ----------------- (1)

Moment of inertia of a body is the product of its mass and the square of radius of gyration.

Here, mass of the diver, m = 140 lb = 140 × 0.453 kg

= 63.5 kg

Radius of gyration, r = 0.3 m

Then, moment of inertia, I = mr²

  = 63.5 × 0.3²

  = 5.7 kgm²

Now, here the angular velocity,

=  1220 deg/s = 1220 ×   rad/s

= 21.29 rad/s

Now, substituting the values in equation (1), we get,

Angular momentum, L = 5.7 × 21.29 = 121.4 kgm²/s.