Question

A couple consisting of two forces $F_1$ and $F_2$ each equal to $5\text{N}$ is acting at the rim of a disc of mass $2\text{kg}$ and radius $0.5\text{m}$ for $5\text{s}$. Initially, the disc is at rest, the final angular momentum of the disc is

• A. $15\text{Nm-s}$
• B. $20\text{Nm-s}$
• C. $25\text{Nm-s}$
• D. $30\text{Nm-s}$

Answer 1

The correct option is C $25\text{Nm-s}$

Torque acting on disc is,
$\tau =F_{1}r+F_{2}r=5\times \frac{1}{2}+5\times \frac{1}{2}=5\text{Nm}$
From angular impulse momentum theorem,
$\underset{0}{\overset{5}{\int }}\tau dt=L_f-L_i$
$\Rightarrow 5\times 5=L_f-0\Rightarrow L_f=25\text{Nm-s}$