Question

For the graph shown below, find the net change in angular velocity of the body during the entire motion.

• A. $12\text{rad/s}$
• B. $-12\text{rad/s}$
• C. $0\text{rad/s}$
• D. $24\text{rad/s}$

Answer 1

The correct option is C $0\text{rad/s}$

Area under $\alpha -t$ graph gives change in angular velocity
Total area = Area of $\Delta AOP+$ Area of rectangle $ABPQ+$ Area of $\Delta BQC+$ Area of $\Delta CRD+$ Area of rectangle $DERS+$ Area of $\Delta EFS$
$=\frac{1}{2}{b}_1{h}_1+b_2{h}_2+\frac{1}{2}{b}_3{h}_3+\frac{1}{2}{b}_4{h}_4+b_5{h}_5+\frac{1}{2}{b}_6{h}_6$
$h_1=h_2=h_3=2{\text{rad/s}}^2\&$
$h_4=h_5=h_6=-2{\text{rad/s}}^2$
$\Rightarrow$ Total area $=\frac{1}{2}\times 4+4\times 2+\frac{1}{2}\times 4-\frac{1}{2}\times 4-4\times 2-\frac{1}{2}\times 4$
$=2+8+2-2-8-2=0\text{rad/s}$