What is the angular momentum of a rod with a mass of #2 kg# and length of #9 m# that is spinning around its center at #12 Hz#?

1 Answer
Jun 26, 2018

The angular momentum is given by

#vec L=Ivec omega#

where

#I="moment of inertia " (kg*m^2)#

#omega="angular velocity "("rad/s")#

For a thin rod with uniform density rotating about the centre, the moment of inertia is given by

#I=1/12*ML^2#

#M="the total mass of the rod "(kg)#

#L="length of the rod "(m)#

You can find moment of inertia formulas for different shaped objects tabulated. In this case

#I=1/12*2*9^2=13.5 " kg"*m^2#

We want to work in SI units, so convert the frequency to angular velocity using

#omega=2pif=2pi*12=24pi " rad/s"#

This arises because each rotation is #2pi# radians and there are 12 rotations per second, so you are rotating through #24pi# radians per second.

Finally, substitute these values into the equation to calculate the angular momentum

#vec L=Ivec omega=13.5*24pi=1017.876=1.02*10^3" "(" kg"*m^2)/s#

Notice that we ditch the radians in the units. This is a a thing that I don't really understand but is due to the definition of the radian being a ratio of two lengths (so units cancel out). It gets used and dropped sporadically.

#equalrightsforallunits

Careful with significant figures too.