Module I
Angular Momentum

Page 332: Questions # 1 to 6 inclusive [answers in bold print]

1.    Give an example in human movement of a system that has angular momentum; tell what factors comprise its angular momentum.

Anything rotating has angular momentum: a rotating body segment, a spinning dancer, a spinning baseball or discus, a swinging gymnast.  Angular momentum is the product of the object's rotational inertia relative to the axis of rotation and its angular velocity.

2.    Define angular impulse.

Angular impulse is analogous to linear impulse; it is the torque applied to a system times the time during which that torque is applied.

3.    Identify the angular impulse that causes a body segment to rotate and therefor gain angular momentum.  Identify the angular impulse that is responsible for diminishing a segment's angular momentum to zero.

Body segments can be rotated by muscle forces or by forces outside the body.  The angular impulse is the force applied at some distance from the joint axis (thereby creating torque times the time that torque is applied.  Once rotating, a segment has angular momentum (rotational inertia times angular velocity), and would continue to rotate with that angular momentum if it were not decelerated by a decelerating torque (muscle or other source) acting for a time.

4.    Hold a book in each hand with the arms held horizontally out from your sides.  Turn and spin on one foot.  While spinning, bring both books to your chest.  Explain the body's motion response in terms of the conservation of angular momentum.

When the book mass is positioned far from the axis of rotation (a vertical axis running through the supporting foot), the body's rotational inertia is large.  The ground reaction friction force on the foot pushing off to spin provides the torque to give the body angular momentum with a relatively slow angular velocity.  When the books are brought toward the axis, the rotational inertia of the body is decreased and the angular velocity of the body must increase to conserve the total angular momentum (assuming floor friction negligible).

5.    Repeat the steps in question 4, but return the arms out to the sides just after you bring the books to your chest.  Explain the response.

If the mass is "spread out" after fast spinning occurs, the angular velocity will decrease because the rotational inertia is increased.

6.    Describe several examples in sport and dance in which the angular momentum of the body is conserved although the angular velocity changes.

In any type of spinning or twisting about the body's long axis, the angular velocity may be the axis (if no external torque is acting, such as when the body is free of support).  Similarly, in diving or aerial stunts in gymnastics, somersault rate of rotation may be increased by piking or tucking from a straight position and may be decreased by "opening up" from a closed position.