What is the angular momentum of a rod with a mass of # 8 kg# and length of #4 m# that is spinning around its center at #12 Hz#?

1 Answer
Dec 23, 2016

Answer:

The answer is #256pi# #kgm^2/s# which to the nearest whole number is 804 #kgm^/s#

Explanation:

Angular momentum is similar in formula to linear momentum:

#L=Ixxomega# as compared to #p =m xx v#

To find the moment of interia #I#, most students would check a list of known expressions, as every different geometry and even a different axis of rotation will play a part in determining the nature of #I#.

In the case of a rod being rotated about its centre, the moment of inertia is

#I=(mL^2)/12#

#L# being the length of the rod, and #m# its mass.

The angular velocity #omega# is equal to the number of radians swept out by the rod each second. In this case, as each revolution equals #2pi# radians,

#omega=24pi #

Put it together:

#L=((mL^2)/12)xx 24pi# = #((8)(4^2)(24pi))/12# = #256pi" " kgm^2/s#

which is approximately 804 #kgm^2/s#