Rotations Free of Support Most common in Dance, Diving, Figure Skating, Gymnastics, Trampoline ML Axis see [Figure 15.2a] L axis see [Figure 15.2b] AP axis see [Fig. 15.2c] flight path of CG determined @ takeoff airborne segmental motions do not change CG flight path [see Figure 15.1 on page 494

Rotations about ML Axis - page 495 FIG 15.2a

Rotations about L Axis - page 496 FIG 15.2b

Rotations about AP Axis - page 496 FIG 15.2c

CG Flight Path determined @ takeoff page 494 FIG 15.1

I is rotational inertia - a body’s resistance to change angular motion L: Angular Momentum L = I   is angular velocity I is rotational inertia - a body’s resistance to change angular motion I = mk² (mass x distance² of mass from axis of rotation)

L stays constant while airborne  changes due to changes in I Conservation of L L stays constant while airborne  changes due to changes in I k changes as body moves to pike position then back to a layout position Fig I.5 page 329

L = I in Body Rotations I (rotational inertia) = mk² Angular Momentum = Rotational Inertia x  I (rotational inertia) = mk² 1. [m] mass of performer (does not change) 2. [k] radius of gyration of performer’s mass 3. [] angular velocity of performer’s rotation distribution of m is key feature

L constant while airborne individual segments may redistribute total body’s L rotate arms forward, trunk rotates backward so total L remains constant LJ - rotate trunk downward and legs move upward L is established @ takeoff the entire body has L L remains constant during flight until an external T acts on body [e.g. floor, water]

Small segment requires   Entire body/system has a magnitude of L created @ takeoff L = I  or L = (mk²) x () L @ takeoff due to magnitude of both I and   @ takeoff due to magnitude of T applied m and k of arms much smaller than total body to slow/stop trunk rotation, arms rotate with  [arms m and k much less than trunk m and k]

RIGHT-HAND THUMB RULE method of determining vector direction curve fingers of right hand in direction of rotation right thumb points in vector direction of L &  see Figure E.5 on page 113 see Figure 15.4 on page 498

RIGHT HAND THUMB RULE FIG E.5 page 113 FIG 15.4 page 498

Initiating Rotations from the Ground GRF (ground reaction force) applied eccentrically FIG 15.5 Pg 500

Initiating Rotations from the Ground GRF (ground reaction force) applied eccentrically FIG I.1b Pg 327

Initiating Rotations from the Ground GRF (ground reaction force) applied eccentrically FIG I.2 Pg 328

Initiating Rotations from the Ground GRF (ground reaction force) applied eccentrically FIG I.3 Pg 328

Initiating Rotations from the Ground GRF (ground reaction force) applied eccentrically Pg 394 FIG 12.5

Initiating Rotations from the Ground GRF (ground reaction force) applied eccentrically page 400 FIG 12.10