# Torque and angular acceleration

I have got 19.6 as the answer for (a) but the book tells 14 is the answer. Can someone tell what mistake I have done or is there in the book.

• hint the force in the rope is not mg. Why? Because the hanging mass is also accelerating. Feb 6, 2018 at 0:34

You omitted the inertia of the mass of $0.5 kg$. The total inertia of the system is the inertia of the disk plus the inertia of the mass.
$$I = \frac{M R^2}{2} + m R^2$$
The total torque about the axle is $T= m g R$. Then use $I \alpha =T$ to get the equation
$$\left(\frac{M R^2}{2} + m R^2\right)\alpha=m g R$$
$$\alpha=\frac{2 g m}{R (2 m+M)}=\frac{(2) (9.8) (0.5)}{(0.2)((2)(0.5)+2.5)}=\frac{9.8}{0.7}=14$$