A string is wrapped around the rim of a wheel of moment of inertia and radius 10 cm. The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of 40 N. The angular velocity of the wheel after 10 s is

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Solution

Q.
A string is wrapped around the rim of a wheel of moment of inertia $0.40$ $k m^{2}$ and radius 10 cm. The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of 40 N. The angular velocity of the wheel after 10 s is $x$ rad/s, where $x$ is _______ . [2024]

Ans.
(100) $τ = F R = I α = 40 \times 0.1 = 0.4 α$

$\Rightarrow α = \frac{4}{0.4} = 10 {rad / s}^{2}$

$ω_{f} = ω_{0} + α t = 0 + 10 \times 10 = 100 rad / s e c .$

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