How Do You Calculate Angular Momentum for a Swinging Bob?

[mburt3]

Homework Statement

The problem asks to calculate the angular momentum for a metallic bob that is suspended from the ceiling by a thread of negligible mass. The angle between the thread and the vertical is 30degrees. It is also given that the mass of the bob is 7 kg and the length of the thread is 2.4m.

Homework Equations

I used the equations:mv^2/r=Tsin(theta)
mg=Tcos(theta)
L=Iw(omega)
I=2/5mr^2

The Attempt at a Solution

I first rearranged mg=Tcos(theta) to solve for T=mg/cos(theta)
Next I substituted this into mv^2/r =Tsin(theta) and got mv^2/r=mgtan(theta)
I found r by using the length of the thread and the angle with the vertical:
sin30= r/2.4 r=1.2
Next I solved for v. v=2.6m/s.
My problem after this was applying it to the equation L=Iw
I knew that L=(2/5)mr^2w or L=2mrv/5 but I wasn't sure what to put for the radius since it was not given.

Am I even on the right track?
Thanks in advance!

 

[horatio89]

Homework Statement

The problem asks to calculate the angular momentum for a metallic bob that is suspended from the ceiling by a thread of negligible mass. The angle between the thread and the vertical is 30degrees. It is also given that the mass of the bob is 7 kg and the length of the thread is 2.4m.

Homework Equations

I used the equations:mv^2/r=Tsin(theta)
mg=Tcos(theta)
L=Iw(omega)
I=2/5mr^2

The Attempt at a Solution

I first rearranged mg=Tcos(theta) to solve for T=mg/cos(theta)
Next I substituted this into mv^2/r =Tsin(theta) and got mv^2/r=mgtan(theta)
I found r by using the length of the thread and the angle with the vertical:
sin30= r/2.4 r=1.2
Next I solved for v. v=2.6m/s.

These should be correct...

My problem after this was applying it to the equation L=Iw
I knew that L=(2/5)mr^2w or L=2mrv/5 but I wasn't sure what to put for the radius since it was not given.

L = I(omega) is correct, but you are using the wrong I. 2/5mr^2 is the moment of inertia of a sphere about an axis through its centre. However, the bob is not rotating about its centre, but rather about a vertical axis at the centre of its circular motion.

Hence I = mr^2, where r is the radius of its circular motion.

 

[mburt3]

Thanks a lot! yea that makes sense. so i guess you can kind of think of it as the moment of inertia of a hollow cylinder?

 

[horatio89]

Not really, we are treating the bob as having the moment of inertia of a single point particle rotating about an axis