Chapter 16
Analysis of Activities, Body Rotating Supported 
 

Page 534: Questions # 1 to 4 inclusive [answers in bold print]

1.    Figure 16.15 shows a system falling around an axis of rotation.  They body's weight is equal to 450 N.  If 1 cm= .1m, what is the torque of the body's weight at points a, b, c, and d?

The torque production of this gymnast's weight will be calcultated by multiplying his weight by its perpendicular distance from the axis of rotation.  Students will find the torque to be zero at position a, and maximum at position d, with position b and position c less than maximum but increasing.

2.    Ignoring friction and air resistance, in which positions in Figure 16.15 should the angular velocities be identical?  In which positions should the angular momenta be identical?  Explain why.

The angular velocity and angular momentum should be identical, when ignoring friction and air resistance forces, at these positions that are opposite each other in the right to left direction; that is, positions b and l; c and k; d and j; e and i; and f and h will have equal angular velocites under these conditions.  The angular impulse used create angular velocity during the descent, will be used to reducte the angular velocity during the ascent.

3.    In Figure 16.15, considering friction forces at the axis of rotation, the positions on the upswing (g through 1) will have an angular velocity less than, equal to, or more than the velocity of the corresponding (opposite) position on the downswing (a through f).  Explain why.

Resistive friction torque and motive weight torque act on the body during descent; but resistive friciont torque and motive weight torque act on the body during descent; but resistive friction torque and resistive weight torque act on the body during ascent.  The net decelerating torque during the ascent is greater than the net accelerating torque during the descent; therefore, the angular velocity of the body will be less than on the downswing.

4.    Observe a runner jogging slowly.  Note the degrees of elbow, hip, knee and ankle flexion during recovery.  Repeat for a medium-speed run and a sprint.  What differences are noticed in the degree of flexion?  Explain the differences in terms of the rotational inertia and muscular torques.

As the speed of a run increases, the rotational inertia of the recovering swinging segments should be reduced so that the recovery may be fast enough to be ready for the next force phase.  The flexing of the extremities during the recovery will reduce their rotational inertia and the extremities may achieve greater acceleration with the amount of muscular torques provided by the flexor muscle groups.