Angular Momentum


To understand how and why systems rotate as they do:

        Angular momentum explains this

Each system resists change in rate of rotation

        This is called rotational inertia (I)

               This varies depending upon the Mass, and the Radius of Gyration

                       - I = mk2, so linear increases with mass,
                                      exponential with radius of gyration

        Angular acceleration is determined by the amount of TORQUE and Rotational Inertia


Systems moving linearly posess a linear momentum (M = mv)

Systems moving angularly posess an angular momentum (L = I*omega = mk2*omega)_

Calculations not presented. but the CONCEPT is Critical

Angular momentum is initially created by an external torque
        This causes a angular velocity (and thus an L)
        We may exert internal torques, but externals cause movement

Primary factor involved in:

               swinging, jumping, throwing, kicking,
               twisting, somersaulting, smimming, and locomotion

        Once the motion begins, 
               movement continues until another torque external to the system stops or speeds
               it up

        Every follow through phase you can think of results from this


To accelerate a body angularly, apply torques

        to acheive a certain angular velocity
               - apply large torque for a short time
               - apply small torque for a long time
        together, these two properties make up ANGULAR IMPULSE (T(t))

Angular Impulse changes the body's angular momentum (I*omega)

        Examples in text:
               hitting a tennis ball, time = short, force is great
               reaction from horse (gymnastics), time is longer, torque is less
               reaction from springboard, time is longest, torque is smaller still

        With standardized (maximal) torque, increase in time with increase Ang. Mom. (L)

Once Angular Momentum is established

        remains constant until acted on by an external torque

        generally, speeds up segments at the beginning of a motion
               and decreases them at the end

When an object speeds up angularly (frisbee, football, top), its stability increases

        Referred to as gyrascopic stability

Conservation of Angular Momentum (L)

        If no external torques are applied to a system, (L) is conserved

        This means that (L), made of I*omega, changes in proportion to I and omega

        Example:
               if make a larger I, omega decreases
               if decrease I, omega increases

        Additional examples:

               I increases:   Opening up from a tuck position in diving
               I decreases:   Closing down in a rotating position