Angular Momentum Angular Velocity and Inertia Angular Momentum

Angular Momentum, Angular Velocity and, Inertia

Angular Momentum l So far you know that: ¡ Angular momentum (Lmom or Ho) is a vector quantity that defines an object’s rotation about an axis of rotation (i. e. any object or fluid that rotates about an axis has angular momentum). It is a measure of the tendency of an object to spin. ¡ Lmom is used to develop kinetic energy and to stabilize moving objects (bike wheel demo) ¡ Lmom is dependent on the object’s mass, radius (inertia) and angular velocity such that Lmom = mrω m=mass, r=radius and ω=angular velocity Units: English = slug. ft 2/s Metric/SI = kg. m 2/s

A Quick Note about Angular Velocity(ω) l Angular velocity (ω) can have units of: A) radians per second (rad/s) – the metric/SI unit or; B) revolutions or rotations per minute (rpm) – the English unit. Interesting pt: The corresponding unit in the International System of Units (SI) is hertz (symbol Hz) or s-1 (1/second). Revolutions per minute is converted to hertz through division by 60. l Often times it is necessary to convert from either rpm rad/s OR rad/s rpm l To convert from rpm to rads simply x by 0. 1047 rad/s* ex. 65 rpm= 65 x 0. 1047 rad/s = 6. 8 rad/s l To convert from rads to rpm simply x by 9. 55 rpm* ex. 6. 8 rad/s= 6. 8 x 9. 55 rpm = 65 rpm *Conversion factors taking from pg. 7 of Engineering Toolbox

A Quick Note about Mass and Radius l When working with angular momentum the product of mass x radius is INERTIA(I) where I=mr l So, the formula L=mrω changes to L=Iω l Thus, the angular momentum of an object is affected by an object’s inertia (mass and radius) and angular velocity. l If shape of object changes, inertia will change (see wkbk p. 43). l For example I=mr 2 for a wheel but I=1/2 mr 2 for solid cylinder. l So, if you are calculating the angular momentum of a wheel L=Iω changes from L=(mr)ω to L=(mr 2)ω l For your spin board activity you assumed that Adam and Jake were cylinders therefore their inertia can be calculated using I=1/2 mr 2. l Therefore, their angular momentum can be calculated using: L= (1/2 mr 2)ω Note: If radius changes (ex. Radius for Arms Out vs Radius for Arms In don’t forget to also use the correct value for “r”)

Working with Angular Momentum Simple Angular Momentum l Let’s calculate simple angular momentum (as you did in your activity) l Let’s try another example: A 900 kg cylindrically shaped communications satellite is launched into orbit from the space shuttle. The satellite’s radius is 0. 7 m. It spins about its own axis at 30 rpm. What is the: a) moment of inertia of the satellite b) angular momentum of the spinning satellite due to its spin? Classwork/Homework: Complete pp. 55 -57 (Let’s review units a-d and Problems 1 -3) *Whatever is not completed in class must be done for homework