Chapter 15
Analysis of Activities with Body Rotating Free
 
Page 499: Questions # 1 to 6 inclusive [answers in bold print]

1.    For the following segmental movements, state the segmental axes about which the segment is rotating; what effect (increase, decrease, remain the same) does the segmental movement have on the body's radius of gyration about each of the three body's axes?

    a.    arm abduction to 90 degrees
    b.    arm flexion to 90 degrees
    c.    knee flexion to 90 degrees
    d.    transverse flexion (adduction) from 90 degrees abduction
    e.    lateral trunk flexion of 70 degrees
    f.    trunk by hyperextension of 40 degrees

a.    A-P axis; increases the radius of gyration about the body's A-P axis, increases the radius of gyration about the body's A-P axis and increases the radius of gyration about the body's Longitudinal axis.

b.    M-L axis; increases the radius of gyration about the body's M-L axis, increases the radius of gyration about the body's A-P axis and increases the radius of gyration about the body's Longitudinal axis.

c.    M-L axis; decreases the radius of gyration about the body's M-L and A-P axes and increases the radius of gyration about the body's Longitudinal axis.

d.    M-L axis of the shoulder joint; increases the radius of gyration about the body's M-L axis, decreases the radius of gyration about the body's A-P axis and effects no change in the radius of gyration about the body's Longitudinal axis.

e.    A-P axis; effects no change in the radius of gyration of about the A-P axis, decreases the radius of gyration about the body's M-L axis and increases the radius of gyration about the body's Longitudinal axis.

f.    M-L axis; decreases the radius of gyration about the body's M-L axis, decreases the radius of gyration about the body's A-P axis and increases the radius of gyration about the body's Longitudinal axis.

2.    How many mass units of resistance to changes in horizontal motion will a body weight 400N have?

The mass of a body is determined by dividing its weight by the acceleration due to gravity.  400/9.8= 40.8

3.    How many mass units of resistance to changes in vertical motion will a body weight 400 N have?

The mass units of resistance in vertical motion would be the same as in horizontal motion:  40.8 mass units of resistance.  In addition to the mass resistance, the weight of the body would have to be counteracted by a greater force to move the body upward.

4.    If a body has 2 mass units and a radius of gyration of 5 cm, what is the rotational inertia if 2 mass units and a 10-cm radius of gyration?

Rotational inertia is the mass times the squared radius of gyration.  The rotational inertia is 2(5)^2 = 50 rotational inertia units; 2(10)^2-200 rotational inertia units.

5.    What is the change in resistance to rotaion of a body with an increase of the radius of gyration to three times what it was initialy a decrease of the radius of gyration to one fourth of what it was?

Since the radius of gyration has a squared effect on the rotational inertia, a three fold increase in the radius of gyration will produce a nine fold increase in the rotational inertia; a decrease in the radius of gyration to 1/4 will produce a 16 fold decrease in the rotational inertia and thus the resistance of the body to changes in rotational motion.

6.    If angular momentum is equal to zero at takeoff, indicate about which axis and in which direction the trunk will move with the following limb movements: (a) circumduction (circling) of the upper extremities forward, (b) circumduction of the upper extremities backward, and (c) abduction of the right upper extremity and adduction of the left upper extremity.

a.    Circumducting the upper extremites forward about a frontal axis through the shoulder joints will cause a backward rotation of the body about the body's frontal axis.

b.    Circumducting the upper extremites backward about a frontal axis through the shoulder joint will cause a forward rotation of the body about the body's frontal axis.

c.    Abduction of the right and adduction of the left upper extremities take place about the sagittal axes of the shoulder joints; therefore, the body will be rotated in the opposite direction (to the body's right) about the body's sagittal axis.

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Page.509: Questions # 1 to 4 inclusive [answers in bold print]

1.    What three body positions identify the cat-rotation method of twisting?

Side arch, back arch, and pike

2.    If one wants to cause forward rotation of the body during flight, what directions would you rotate your upper extremities to cause a forward reaction rotation of your body?

Backward

3.    What position of the body is required for one "twist from a somersault" technique?

Asymmetrical

4.    Which of the three twisting techniques produces the greates amount of rotation with the least amount of effort?  Which produces the least twisting for the greatest effort?

Twist from a somersault
Reaction rotation
 
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Chapter 15 continued (pp. 509-517)
Analysis of Activities with Body Rotating Free
 

Pages 516-517: Questions # 1, 2, 3, 4, 7 [answers in bold print]
 
1.    For the following changes in the radius of gyration, k, state the change in the angular velocity that would be effected:  (a) 1/3 k, (b) 1/5 k, (c) 6 k, (d) 12 k

a.    A decrease in the radius of gyration to 1/3 its original size would cause an increase in the angular velocity of 9 times.

b.    A decrease in the radius of gyration to 1/5 its original size would produce a 25 fold increase in the angular velocity.

c.    If the radius of gyration is increased 6 times, the velocity will decrease to 1/36 its original value.

d.    An increase in the radius of gyration of 12 times would cause a decrease in the angular velocity to 1/144 its original value.

2.    If a performer can do two somersaults in a layout position, how many somersaults can be done in a tight tuck in a medium pike?  Use Table 15.1 on page 510.

In order to use Table 15.1, find the takeoff position in the left hand column, labeled starting positions.  Read across the row to the column of the assumed position.  This is the factor of the original rotation.

a.    From a layout to a tight tuck, the factor is 4.67; therefore the body will perform 2 times 4.67 rotations, or about 9.3 rotations.

b.    From a layout to a medium pike, the factor is 3.22; therefore the body will perform 2 times 3.22 rotations, or about 6.4 rotations.

3.    To affect as much change as possible in the angular velocity, a performer should leave the support in what positions?  Why?

If a perfomer wants to effect as much increase as possible in the angular velocity, the body should leave the supporting surface in a position that has the greatest potential for change, that is, in a position with the greatest radius of gyration about the axis of rotation.  For example, a layout position with the arms over the head for potentially increasing the angular velocity about the frontal axis, or with the arms and legs abducted fore potentially increasing the angular velocity about the longitudinal axis.

4.    Discuss the problems a freestyle skier would have in attempting to initiate a reaction rotation about the longitudinal axis, as compared with a gymnast attempting the same rotation.

Because the freestyle skier has a greater rotational inertia about the frontal and longitudinal axes due to the mass and legnth of the skis, the skier's turing velocity will be less affected by segmental movements than a gymanst's body performing the same actions.

7.    Kane and Scher (1970) estimated that circumducting the arms forward once would cause a 12 degree backward rotation of the body with the legs extended and 24 degree backward rotation of the body with the legs tucked.  Why is there a difference?

"Tucking" the legs reduces the body's radius of gyration about its M-L axis.  Thus, for one complete circumduction of the arms about their M-L axes, a greater response is proudced.  When the legs are extended the body's radius of gyration about its M-Laxis is increased; therefore, a complete circumduction of the arms produces a smaller total body response.