Instantaneous Veloctiy, kinda hard Help

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In summary, the conversation discusses the problem of finding the instantaneous speed of a 2.00kg mass whirling on a string on a horizontal frictionless surface. The string is slowly winding around a vertical rod and its length has shortened from .750m to .250m. The conversation explores different formulas, including I = mr^2 and L = Iw, to solve the problem, ultimately arriving at the correct answer of 80 m/s by using the formula L/I = w and correcting an error in arithmetic.
  • #1
Sucks@Physics
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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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  • #2
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.]
 
  • #3
L=Iw? I'm still kind of lost...
 
  • #4
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]
 
  • #5
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?
 
  • #6
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.)
 
  • #7
Awesome! I got it thanks a lot!
 

1. What is instantaneous velocity?

Instantaneous velocity is the velocity of an object at a specific moment in time. It is a measure of how fast an object is moving and in which direction at a single point in time.

2. How is instantaneous velocity different from average velocity?

Instantaneous velocity is the velocity at a specific moment, while average velocity is the total displacement of an object over a period of time. Average velocity takes into account the entire motion, while instantaneous velocity only considers one moment.

3. How is instantaneous velocity calculated?

Instantaneous velocity is calculated using the formula V = limΔt→0 Δx/Δt, where V is the instantaneous velocity, Δx is the change in position, and Δt is the change in time. This formula is based on the concept of finding the slope of the tangent line at a specific point on a position vs. time graph.

4. Can instantaneous velocity be negative?

Yes, instantaneous velocity can be negative. This indicates that the object is moving in the negative direction, such as moving south or backwards. It is important to pay attention to the direction of the velocity, as it provides valuable information about the motion of an object.

5. How is instantaneous velocity related to acceleration?

Instantaneous velocity and acceleration are related through the equation a = dv/dt, where a is acceleration, v is velocity, and t is time. This means that the acceleration of an object is the rate of change of its velocity over time. In other words, acceleration is the change in instantaneous velocity over time.

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