Instantaneous Veloctiy, kinda hard Help

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Homework Help Overview

The problem involves a mass moving in a circular path with a changing radius due to a string winding around a rod. Participants are exploring the concept of instantaneous velocity as the string length decreases from 0.750 m to 0.250 m, while considering the implications of angular momentum and its conservation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the conservation of angular momentum and how to compute it for a point mass. There are questions about the relationship between angular momentum, moment of inertia, and angular velocity. Some participants express confusion about the calculations and the assumptions being made regarding the system.

Discussion Status

The discussion is active, with participants attempting to clarify their understanding of angular momentum and its application to the problem. Some guidance has been offered regarding the relationships between variables, but there is no explicit consensus on the correct approach or resolution of the problem.

Contextual Notes

There are indications that assumptions about the conservation of angular momentum may not hold due to the changing angle of the string with respect to the radius. Participants are also encouraged to recheck their calculations as they work through the problem.

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Initially, a 2.00kg mass is whirling at the end of a string in a circular path of .750 m on a horizontal frictionless surface with a tangential speed of 5 m/s. The string has been slowly winding around a vertical rod, and a few seconds later the length of the string has shortened to .250 m. What is the instantaneous speed of the mass at the moment the string reaches a length of .250m.

I = mr^2 but i must be missing a formula because that won't work because it would give me a smaller number and it obviously speeds up the shorter the string gets.
 
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angular momentum

What they undoubtedly want you to assume is that angular momentum is conserved. How do you compute the angular momentum of a point mass?

[Note well: Unfortunately, this problem is bogus since the string makes an angle with the radius as it wraps around the pole and angular momentum is not conserved. No work is done on the system so its speed cannot change. But I suggest that you ignore that inconvenient fact and carry on.]
 
L=Iw? I'm still kind of lost...
 
Sucks@Physics said:
L=Iw?
That's a perfectly OK way to approach it (but not the only way). What's I? What's w? (How does w relate to tangential speed?)

[tex]I_1 \omega_1 = I_2 \omega_2[/tex]
 
v/r =w and I = mr^2 so...

I = 2kg*.750^2 = 1.125
5m/s/.750 = 6.667
L=1.125*6.667 = 7.5

I=2kg*.250^2 =.125

7.5/.125 = 80 m/s

Where did i mess up?
 
Sucks@Physics said:
7.5/.125 = 80 m/s

Where did i mess up?
(1) Recheck your arithmetic.
(2) L/I = w, not v. (But w = v/r.)
 
Awesome! I got it thanks a lot!
 

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