Question

A cord is wrapped around the rim of a flywheel $0.5m$ in radius and a steady pull of $50N$ in applied on the cord as shown in the figure. The wheel is mounted on a frictionless bearing on the horizontal shaft through its centre. The moment of inertia of the wheel is $4kg{m}^2$.
(a) Compute angular acceleration of the wheel
(b) If a mass having a weight $50N$ hangs from the cord as shown in the figure. Compute the angular acceleration of the wheel. Why is this not the same as in part (a)?

Answer 1

$\left(a\right)$ $\propto =\frac{\tau }{1}=\frac{(50N\times 0.5m)}{4kg{m}^2}=6.25rad{s}^{-2}$

$\left(b\right)$ $R\times mg=I\propto$

$\therefore 0.5m\times 50N=4\times \propto$

$\therefore \propto =\frac{0.5\times 50}{4}$

$=6.25rad{s}^{-2}$

$\therefore$ Both the angular acceleration is equal