   Chapter 8, Problem 55P

Chapter
Section
Textbook Problem

The top in Figure P8.55 has a moment of inertia of 4.00 × 104 kg · m2 and is initially at rest It is free to rotate about a stationary axis AA'. A string wrapped around a peg along the axis of the top is pulled in such a manner as to maintain a constant tension of 5.57 N in the string. If the string does not slip while wound around the peg, what is the angular speed of the top after 80.0 cm of string has been pulled off the peg? Hint: Consider the work that is done. Figure P8.55

To determine
The angular speed of the top after 80.0cm of string has been pulled off the peg.

Explanation

Given info: The moment of inertia of the top is 4.00×104kgm2 , the constant tension in the string is 5.57N , and length of the string that has been pulled off the peg is 80.0cm .

Explanation: From work-energy theorem, the angular speed of the top is calculated that is Wnet=Fs=KEfKEi=12Iωf20 since ωi=0rad/s .

The formula for the angular speed of the top after 80.0cm of string has been pulled off the peg is,

ωf=2FsI

• F is constant tension in the string.
• s is length of the string that has been pulled off the peg.
• I is moment of inertia of the top.

Substitute 5.57N for F , 80

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