A fun new circular motion question

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Homework Help Overview

The discussion revolves around a circular motion problem involving the relationship between linear speed and angular speed. The original poster attempts to derive the linear speed using the formula \(9.8 = \frac{v^2}{r}\) and expresses confusion regarding the conversion from meters per second to radians per second.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of linear speed and its conversion to angular speed, questioning the original poster's method and understanding of the variables involved. There is also a focus on clarifying the definition of the radius used in the calculations.

Discussion Status

The conversation is ongoing, with participants providing clarifications about the definitions of linear and angular speed. There is a lack of consensus on the correct approach to the problem, as multiple interpretations of the calculations and definitions are being explored.

Contextual Notes

Participants note the conversion of radius from miles to meters and the potential confusion surrounding the units of measurement. The original poster expresses uncertainty about the correctness of their calculations and the definitions of the variables.

Garen
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Ok, so I set 9.8=v^2/r , therefore v=\sqrt{9.8r}. I converted r from miles into meters and got 3459.35. This seems like an easy enough question, but for some reason I keep getting it wrong. The answer I keep getting is 184.12395m/s, but the question asks for it in rad/s. I've looked everywhere on how to convert m/s to rad/s, but no luck. I don't know if the problem is the conversion or my method in attaining v. Also is v=angular speed? Thanks in advance to all you physics geniuses out there.
 
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BUMP for help please.
 
v is linear speed in m/s. The angular speed in radians/s=v/r.
 
Dick said:
v is linear speed in m/s. The angular speed in radians/s=v/r.

So what you're saying is that I set 9.8=v/(radius of cylinder) ?

(3459.35)(9.8)=v

33901.73=v=angular speed in rad/s

Is this correct?
 
No, no, no. You found v. The angular velocity is v/r.
 
Dick said:
No, no, no. You found v. The angular velocity is v/r.

Could you define r?
 
Garen said:
Could you define r?

Radius :)

2.15 mi.
 
Last edited:
Garen said:
Could you define r?

The same r you used in v^2/r. It's your notation.
 

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