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Systems of Particles and Rotational Motion — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsSystems of Particles and Rotational Motion3 Marks
Question
A cylinder of length 20cm and radius 10cm is rotating about its central axis at an angular speed of 100rad/s. What tangential force will stop the cylinder at a uniform rate in 10 seconds? The moment of inertia of the cylinder about its axis of rotation is 0.8kgm2.
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Answer

$\alpha=\frac{\omega-\omega_0}{\text{t}}=-10\text{rad/s}^2$
$\text{F.R}=\text{I }\alpha$
$\text{F}=\frac{\text{I }\alpha}{\text{R}}$
$=\frac{(0.8\text{kgm}^2)(-10\text{rad/s}^2)}{0.1\text{m}}=-80\text{N}.$

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