Answer to Question #313367 in Mechanics | Relativity for princi

Question

A flywheel has a moment of inertia of 4.8 kg-m2 . What constant force is required to increase its

frequency from 3 rev/s to 6 rev/s in 7 revolutions?

Answer 1

$2\pi N=\frac{\omega_f^2-\omega_i^2}{2\alpha}$

The angular acceleration

$\alpha=\frac{\omega_f^2-\omega_i^2}{4\pi N}=\pi\frac{n_f^2-n_i^2}{N}$

$\alpha=3.14\times\frac{6^2-3^2}{7}=12.1\:\rm rad/s^2$

The requrid torque

$\tau=I\alpha\\ =4.8\times 12.1=58\:\rm N\cdot m$