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# A solid uniform cylinder with mass $8.25 \mathrm{~kg}$ and diameter $15.0 \mathrm{~cm}$ is spinning at $220 \mathrm{~rpm}$ on a thin, frictionless axle that passes along the cylinder axis. You design a simple friction brake to stop the cylinder by pressing the brake against the outer rim with a normal force. The coefficient of kinetic friction between the brake and rim is $0.333$. What must the applied normal force be to bring the cylinder to rest after it has turned through $5.25$ revolutions?

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$\large{\text{PROBLEM:}}$

To find the applied normal force to bring the cylinder to rest after it has turned through 5.25 revolutions.

$\large{\text{GIVEN:}}$

• Mass of the disk: $m = 8.25\;\text{kg}$
• Radius of the disk: $R = 0.0750\;\text{m}$
• Initial angular speed: $\omega_0 = 0$
• Final angular speed: $\omega= 220\;\text{rpm}$
• Number of revolutions: $\theta - \theta_0 = 5.25\;\text{rev}$
• Coefficient of friction: 0.333

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