Answer to Question #120544 in Classical Mechanics for kebone

Question

Two disks with the same inertia 1kg are rotating along the same axis.
• Disk A has radius 2m and disk B has radius 4m.
• Disk A is rotating with 2rad/s, ω direction up
• Disk B is rotating with 1rad/s, ω direction down
• Now the two disks are jointed together, calculate
the final angular momentum of the combined disks

Answer 1

As per the given question,

Two disk have the same inertia it means $m_1=m_2=1 kg$

The radius of the disk A $(r_1)=2m$

and radius of the disk B$(r_2) =4m$

angular velocity of the disk A is $(\omega_1)=2rad/sec (upward)$

Angular speed of the disk B is $(\omega_2)=1 rad/sec(downward)$

Two disks are getting joined, let the final angular speed if $\omega$

Applying the conservation of angular momentum,

$I_1\omega_1-I_2\omega_2=(I_1+I_2)\omega$

$\Rightarrow \omega=\frac{I_1\omega_1-I_2\omega_2}{I_1+I_2}$

$\Rightarrow \omega=\frac{m_1r_1^2 \omega_1-m_2r_2^2\omega_2}{m_1 r_1^2+m_2 r_2^2}$

$\Rightarrow \omega=\frac{8-16}{4+16} rad/sec$

$\Rightarrow \omega=\frac{-8}{20}=-0.4 rad/sec (downward)$