The top in figure has a moment of inertia of $$4.00$$ x $$10-4kg$$.$$m2$$ and is initially at rest. It is free to rotate about the 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 $$2.5$$ 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?

Question

The top in figure has a moment of inertia of $$4.00$$ x $$10-4kg$$.$$m2$$ and is initially at rest. It is free to rotate about the 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 $$2.5$$ 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?

Infinity Learn · Accepted Answer

For the $$non-isolated$$ system of the top,⇒ W $$=$$ ∆K ⇒F∆x $$=$$ (12I$$ω$$2-0)ω $$=$$ $$2F$$ ∆xl $$=$$ $$2(2.5N)(0.800$$ $$m)4$$×$$10-4kg$$.$$m-2$$ $$=$$ $$100$$ $$rad/s$$

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