1. Tardigrade
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  4. The top in figure has a moment of inertia of 4.00 × 10-4 kg ⋅ m 2 and is initially at rest. It is free to rotate about the stationary axis A A prime . 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 2.5 N. If the string does not slip while it is unwound from the peg, what is the angular speed of the top after 80.0 cm of string has been pulled off the peg?

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Q. The top in figure has a moment of inertia of $4.00 \times$ $10^{-4} kg \cdot m ^{2}$ and is initially at rest. It is free to rotate about the stationary axis $A A^{\prime} . A$ string, wrapped around a peg along the axis of the top, is pulled in such a manner as to maintain a constant tension of $2.5 N$. If the string does not slip while it is unwound from the peg, what is the angular speed of the top after $80.0 \,cm$ of string has been pulled off the peg?Physics Question Image

System of Particles and Rotational Motion

Solution:

For the non-isolated system of the top,
$\Rightarrow W =\Delta K \Rightarrow F \Delta x=\left(\frac{1}{2} I \omega^{2}-0\right) $
$ \omega =\sqrt{\frac{2 F \Delta x}{I}}=\sqrt{\frac{2(2.5\, N )(0.800 \,m )}{4 \times 10^{-4} kg \cdot m ^{2}}}=100 \,rad/s $