How Do You Calculate Angular Momentum for a Swinging Bob?

AI Thread Summary
To calculate the angular momentum of a swinging bob, the problem involves a 7 kg bob suspended by a 2.4 m thread at a 30-degree angle. The tension in the thread is derived from the equations T = mg/cos(theta) and mv^2/r = Tsin(theta), leading to a calculated velocity of 2.6 m/s. The moment of inertia used in the angular momentum formula L = Iω must be corrected; instead of using I = (2/5)mr^2, the appropriate moment of inertia for the bob is I = mr^2, treating it as a point mass. The radius for angular momentum calculations corresponds to the radius of circular motion, which is 1.2 m. Understanding these concepts is crucial for accurately calculating angular momentum in this scenario.
mburt3
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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!
 
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mburt3 said:

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...

mburt3 said:
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.
 
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?
 
Not really, we are treating the bob as having the moment of inertia of a single point particle rotating about an axis
 

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