Angular Momentum Problem

  • Thread starter mburt3
  • Start date
  • #1
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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!
 

Answers and Replies

  • #2
101
0

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.
 
  • #3
23
0
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?
 
  • #4
101
0
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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