Why Is My Calculation of a Cone's Angular Momentum Incorrect?

[dowjonez]

I have already got help with figuring this out. But i seem to be getting something wrong so maybe someone can check this over and tell me what I am doing wrong

Q) find the angular momentum of a cone with heigh H and radius R


now i was helped and told

Mass of cone is integral of the "mass density" within the volume.
center-of-mass uses the same "mass density" and volume limits,
but multiplying the volume element by its location.
Rotational Inertia is the same mass density and same limits,
but multiplies the volume element by r^2 from the axis.
(the omega is the same for all points on the rigid body.)

Rc = int (x)dv / int dV where (x)dV is the volume element and int dV is the mass density

now dV = pi (rx/h)^2 for a cone


so i did angular momentum = int (r^2)dV / int dV


where int (r^2)dV = pi int of (r^4 x^2 / h^2) dR
= pi (r^5 X^2 / 5 h^2)

and


mass density = pi ( r^3 x^2 / 3 h^2)


so I = 3/5 r^2





but I am getting froma book I = 3/10 m r^2 for a cone





please HELP!

tell me if u can't understand this

 

[Tide]

Check this out: http://scienceworld.wolfram.com/physics/MomentofInertiaCone.html

 

[quicknote]

Based on the information provided, it seems like you have made a mistake in your calculation for the angular momentum of a cone. The correct formula for the angular momentum of a cone is I = 3/10 m r^2, where m is the mass of the cone and r is the radius. It seems like you have used the incorrect formula for the moment of inertia, which is the rotational inertia of a cone. The correct formula for the moment of inertia of a cone is I = 3/5 m r^2. This means that your calculation for the angular momentum should be I = 3/10 m r^2, which matches with the book's answer. I hope this helps clarify any confusion and helps you to correctly solve for the angular momentum of a cone.