What is the angular momentum of a rod with a mass of #15 kg# and length of #6 m# that is spinning around its center at #23 Hz#?

1 Answer
Jan 19, 2016

Answer:

#vecL=6503.085kg.m^2//s# in direction of #vecrxxvecp#.

Explanation:

The moment of inertia of a thin rod about an axis through its centre is given by (can be proven - ask if you want me to show you the derivation)

#I=1/12ML^2#

#=1/12xx15xx6^2#

#=45kg.m^2#.

The angular velocity of the rod is given by

#omega=2pif#

#=2pixx23=144.513rad//s#.

Hence the angular momentum is given by

#L=Iomega#

#=45xx144.513#

#=6503.085kg.m^2//s#.

The direction hereof may be obtained by the right hand rule - curl the fingers of your right hand in the direction of the rotation and your thumb will point in the direction of the angular momentum #vecL#.