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 #24 Hz#?

1 Answer
Dec 30, 2015

Answer:

# L=81430# #kg.m^2//s#

Explanation:

By definition, angular momentum is the cross product of the position vector from the axis of rotation to the rotating object and the linear momentum of the object.
That is, #vecL=vecr xx vecp# where #vecp=mvecv#.

So in this case, the magnitude of the angular momentum is
#L=rmvsin90^@#
#=6xx15xx((2pi6xx24)/1)#, since #v=x/t# and the object completes 24 circumferences or cycles per second).
#therefore L=81430kg.m^2//s#.

The direction of #L# will be obtained by the right hand rule as per normal vector cross-products - curl the fingers of your right hand from #vecr# to #vecp# and then your thumb will point in the direction of #vecL#, which will be perpendicular to the plane formed by #vecr and vecp#.
So for example if the circular rotation is in the xy-plane formed by the basis unit vectors #hati and hatj#, then the angular momentum will be along the basis unit vector #hatk#.