Kleppner & Kolenkow find the tension of a rotating loop of string

In summary, a high school student is seeking clarification on a problem in their physics textbook. The problem involves finding the tension in a string that is spun at a uniform angular velocity. The solution in the book is T = (M*L*ω^2)/(2π)^2, but the student's answer was T = Mω^2/2π. After receiving feedback, the student realizes they forgot to include a factor R in their expression, which led to the incorrect answer.
  • #1
AlwaysCurious
33
0
Hello, I am a high school student trying to learn physics out of Kleppner and Kolenkow. Unfortunately, the solutions to some of the problems are not available online, nor is a solutions manual available, so I am unable to find out where I am wrong in some cases, such as this one. I would appreciate your clarification.

Homework Statement


A piece of string of length L and mass M is fastened into a circular loop and set spinning about the center of a circle with uniform angular velocity ω. Find the tension in the string.

Homework Equations


The answer in the book states that T = (M*L*ω^2)/(2π)^2, whereas the answer that I got was T = Mω^2/2π.

The Attempt at a Solution


Please the attached pdf - I have tried to write as clearly as possible, and am unable to find how my solution is incorrect. Thank you!
 

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  • #2
A useful check is whether the various items you have expressions for are dimensionally correct. Your final answer has dimensions MT-2, which is wrong for a force.
Apply the same test to your expression ΔθM/L.
 
  • #3
haruspex said:
A useful check is whether the various items you have expressions for are dimensionally correct. Your final answer has dimensions MT-2, which is wrong for a force.
Apply the same test to your expression ΔθM/L.

Thank you! I forgot to include the factor R in there, which gets me where I want to go.
 

Related to Kleppner & Kolenkow find the tension of a rotating loop of string

1. What is the purpose of finding the tension of a rotating loop of string in Kleppner & Kolenkow?

The purpose of finding the tension of a rotating loop of string in Kleppner & Kolenkow is to understand the dynamics of a rotating system and the forces involved. This can be applied to various real-life situations such as analyzing the tension in a rope during a tug-of-war game or understanding the forces acting on a spinning top.

2. How is the tension of a rotating loop of string calculated?

The tension of a rotating loop of string is calculated using the centripetal force formula, which is T = mv^2/r (where T is tension, m is mass, v is velocity, and r is radius). This formula takes into account the mass of the string, its angular velocity, and the radius of its rotation.

3. What factors affect the tension of a rotating loop of string?

The tension of a rotating loop of string is affected by the mass of the string, its angular velocity, and the radius of its rotation. Additionally, external forces such as friction or gravity may also impact the tension.

4. Can the tension of a rotating loop of string ever be equal to zero?

No, the tension of a rotating loop of string can never be equal to zero. This is because in order for the string to remain in rotation, there must be a force acting on it, and tension is the force that keeps the string in tension.

5. What are some real-life applications of understanding the tension of a rotating loop of string?

Understanding the tension of a rotating loop of string has many real-life applications, such as analyzing the forces involved in a spinning top, understanding the dynamics of a yo-yo, or calculating the tension in a rope during a rock climbing activity. It can also be applied in engineering fields, such as designing and analyzing the tension in rotating machinery.

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