Angular Momentum of a conical pendulum

[Momentum09]

Homework Statement

A small metallic bob is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal circle so that the thread describes a cone.
Given: Length of string = 2.8m
Angle between string and vertical: 21 degrees
Mass of bob: 2.9kg

Homework Equations

I = mr^2
w = square root of [g/(lcos(theta)]
Momentum = I x w

The Attempt at a Solution

I first calculated the angular velocity by plugging numerical values into the equation and got 1.936 rad/s. Then, I found out the moment of inertia of the bob by multiplying 2.9 x 2.8^2 [this is the step I'm not sure of], but the answer wasn't right. Is there something I missed out?
Thank you for your help!

 

[Harmony]

The raidus is wrong. It should be r * theta

 

[m2003]

Hello, the moment of inertia for a conical pendulum is not simply the mass multiplied by the length of the string squared. The formula for the moment of inertia of a conical pendulum is I = mr^2sin^2(theta), where r is the length of the string and theta is the angle between the string and the vertical. Therefore, in this case, the moment of inertia would be 2.9 x 2.8^2 x sin^2(21) = 5.08 kg*m^2. This should give you the correct answer for the angular momentum. I hope this helps!