Question

For the Atwood machine depicted above, the mass of the pulley wheel is $50g,r=25cm,R=50cm,m_1=125g$ and $m_2=150g$. The mass of the rope and frictional effects are negligible.
If the pulley wheel starts from rest, what is the angular momentum of the pulley wheel after $5.0s$?

• A. $2.14kg\frac{m^2}{s}$
• B. $-2.14kg\frac{m^2}{s}$
• C. $6.13kg\frac{m^2}{s}$
• D. $-6.13kg\frac{m^2}{s}$
• E. $8.20kg\frac{m^2}{s}$

Answer 1

The correct option is A $2.14kg\frac{m^2}{s}$

$theMOIofpullysystem=m{R}^2+m_1{r}^2+m_2{R}^2={(50\times 50}^2+125\times {25}^2+150\times {50}^2)\times {10}^{-7}㎏/㎡=0.0578㎏/㎡Z=g(m_{2}R-m_{1}r)=g(150\times 50-125\times 25)\times {10}^{-3}{㎏}^2/㎡=0.428{㎏}^2/㎡\alpha =\frac{Z}{I}=7.4rad/s\omega =\alpha t\omega at5sec=37rad/sL=I\omega =2.14㎏m^2/sec$