What is the angular momentum of an object with a mass of #7 kg# that moves along a circular path of radius #4 m# at a frequency of # 4 Hz #?

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1 Answer
Dec 29, 2015

Answer:

#vecL=2814.867kg.m^2//s hatk#

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^@#
#=4xx7xx((2pi4xx4)/1)#, since #v=x/t# and the object completes 4 circumferences or cycles per second).
#therefore L=2814.867kg.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#.