Angular Momentum,Angular Velocity and, Inertia

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Angular Momentum,Angular Velocity and, Inertia
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Angular Momentum

• So far you know that
• Angular momentum (Lmom or Ho) is a vector
  quantity that defines an objects 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 objects mass, radius
  (inertia) and angular velocity such that
  
• Lmom mr?
• mmass, rradius and ?angular velocity
• Units English slug.ft2/s
• Metric/SI kg.m2/s

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A Quick Note about Angular Velocity(?)

• Angular velocity (?) 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.
• Often times it is necessary to convert from
  either rpm ? rad/s OR rad/s ? rpm
• To convert from rpm to rads simply x by
  0.1047rad/s
• ex. 65rpm 65 x 0.1047rad/s 6.8rad/s
• To convert from rads to rpm simply x by 9.55rpm
• ex. 6.8rad/s 6.8 x 9.55rpm 65rpm
• Conversion factors taking from pg.7 of
  Engineering Toolbox

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A Quick Note about Mass and Radius

• When working with angular momentum the product of
  mass x radius is INERTIA(I) where Imr
• So, the formula Lmr? changes to LI?
• Thus, the angular momentum of an object is
  affected by an objects inertia (mass and radius)
  and angular velocity.
• If shape of object changes, inertia will change
  (see wkbk p.43).
• For example Imr2 for a wheel but I1/2mr2 for
  solid cylinder.
• So, if you are calculating the angular momentum
  of a wheel LI? changes from L(mr)? to L(mr2)?
• For your spin board activity you assumed that
  Adam and Jake were cylinders therefore their
  inertia can be calculated using I1/2mr2 .
• Therefore, their angular momentum can be
  calculated using
• L (1/2mr2)?
• Note If radius changes (ex. Radius for Arms Out
  vs Radius for Arms In dont forget to also use
  the correct value for r)

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Working with Angular Momentum

• Simple Angular Momentum
• Lets calculate simple angular momentum (as you
  did in your activity)
• Lets try another example
• A 900kg cylindrically shaped communications
  satellite is launched into orbit from the space
  shuttle. The satellites radius is 0.7m. It spins
  about its own axis at 30rpm. 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 (Lets
review units a-d and Problems 1-3) Whatever is
not completed in class must be done for homework