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Biomechanical
Principles to be Investigated
Newton’s first and second laws of angular motion: conservation of
angular momentum and the relationship among angular acceleration, external
torque applications and rotational inertia
Purpose
A gymnast’s initial linear velocity at the point of take-off from
the spring floor during a tumbling pass is determined by his/her running
velocity. Once airborne, the gymnast becomes a projectile (i.e.,
body is untethered and not in contact with the ground) capable of
performing a variety of tricks (e.g., somersault in the pike, tuck or
lay-out position). The duration of time spent as a projectile is
determined by the initial take-off velocity and the angle of projection of
the center of mass at take-off. The type of somersault performed
while airborne will be determined by the arrangement of the lever segments
about the axis of rotation through the center of mass of the body. Why?
This lab will investigate Newton’s second law as it applies to rotary
motion (i.e., a= T/I) and the law of conservation
of angular momentum by examining a gymnast performing a somersault in the
tuck and layout position during a tumbling pass on the spring floor.
Rationale
Newton’s first law describing angular motion tells us that once a
body/system possesses angular momentum (L) it will be conserved unless
acted upon by an external torque (T). Hence, rearrangement of the body
limbs (requires internal torque applications) about its center of mass
does not affect its angular momentum, but does exert a dramatic effect on
the body’s resistance to rotation (i.e., rotational inertia or I = mk2)
and its ability to revolve about a select axis (i.e., angular velocity or
w=q/t).
Newton’s second law describing angular motion (T=Ia)
tells us that the angular acceleration (a)
of a body, segment or object is directly proportional to the applied net
external torque (T) and is inversely proportional to the rotational
inertia (I) of the body, segment or object.
Thus, the further away from the axis of rotation a system’s mass
is distributed for any given amount of external torque application, the
smaller the angular acceleration it experiences.
On the other hand, the closer a system’s mass is distributed around
its axis of rotation for any given amount of external torque application,
the larger the angular acceleration it experiences.
Gymnasts manipulate the relationship between rotational inertia and
angular velocity expressed in Newton’s first and second laws for
describing angular motion to perform various types of somersaults,
handsprings, etc. during tumbling passes on the spring floor. |
