Instantaneous Veloctiy, kinda hard Help

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SUMMARY

The discussion centers on calculating the instantaneous speed of a 2.00kg mass as it moves in a circular path with a changing radius from 0.750m to 0.250m. The conservation of angular momentum is critical, with the formula L = Iω being applied, where I represents the moment of inertia and ω is the angular velocity. The user initially miscalculated the final speed, arriving at 80 m/s, but was guided to correct their approach by re-evaluating the relationship between angular momentum and angular velocity. Ultimately, the correct interpretation of the formulas led to a clearer understanding of the problem.

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  • Familiarity with the moment of inertia formula, I = mr²
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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?)

I_1 \omega_1 = I_2 \omega_2
 
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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