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Q. 20.2

A wooden top has a moment of inertia of $2.4 × 10^{-5}$ kg $m^{2}$ about its axis. It starts spinning when a string wound round the spindle of the top is pulled with a constant force of 0.5 N. Assuming there is no loss of energy due to friction, find the angular speed attained by the top when the length of the string is 0.3 m.

Verified Solution

The work done in pulling the string is 0.5 × 0.3 = 0.15 J and, as no energy is lost in the process, this is equal to the gain in kinetic energy of the top. So the angular speed attained is ω rad $s^{-1}$, where

$\frac{1}{2} × 2.4 × 10^{-5}$ ω² = 0.15

⇒           ω² = 12 500.

The angular speed is 112 rad $s^{-1}$ correct to 3 significant figures.