Question

152 Rotational collision A O.400 kg A 0.150 kg solid disk with radius 0.050 m rotates at 180 revolutions per minute. ring with radius 0.030m is held at rest and then gently dropped onto the disk so that its center coincides with the center of the disk. It sticks. Determine the angular velocity of the combination after the ring sticks to the disk

Answer 1

$I_i\omega_i=I_f\omega_f$

$\omega_f=\frac {I_i\omega_i}{I_f}$

$I_{i}=\frac {1}{2}mr^2= \frac {1}{2}\times 0.150\times 0.050^2 = 1.875\times 10^{-4}\: kgm^2$

$I_f =m_{ring}r_{ring}^2 +\frac {1}{2}m_{disk}r_{disk}^2=0.400\times 0.030^2+ \frac {1}{2}\times 0.150\times 0.050^2$

$I_f= 5.475\times 10^{-4}\: kgm^2$

$\mathbf{\omega_f =61.64\: rpm}$