How Do You Calculate Angular Momentum for a Rotating Rigid Body?

[math_head7]

Angular Momentum Question?

Homework Statement

Figure 11-45 (attached) shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 2.5s. Assuming R=0.50m and m=
2.0kg, calculate (a) the structure's rotational inertia about the axis of rotation and (b) its angular momentum about that axis.

Homework Equations

I=$$\int$$r²dm
L=I_$$\omega$$

The Attempt at a Solution

(a) I did mr² = (10)(.5)² = 2.5 (the answer is supposed to be 1.6
Then I tried m_sr_s² + m_cr_c² = (8)(.25)² + (2)(.5)² = 1.5 (still incorrect)

(b) Due to not being able to solve "a" I could not began my attempt on "b"

 

[Doc Al]

(a) I did mr² = (10)(.5)² = 2.5 (the answer is supposed to be 1.6
Then I tried m_sr_s² + m_cr_c² = (8)(.25)² + (2)(.5)² = 1.5 (still incorrect)

Not sure what you're doing here. The thin rods and the hoop are standard shapes--you can look up their rotational inertia. (You'll need to use the parallel axis theorem.)

 

[cupid.callin]

first find I of hoop along any diameter using perpendicular axis theorem and then use parallel axis theorem to find I along axis of rotation
do same for square

then just simply add their I

 

[math_head7]

Thanks. I got it.