Question

a child of mass 50kg is standing an the edge of merry gi round of mass 250kg and radius 3m which is rotating with an angular velocity of 30rad/sec . what will be the final angular velocity of the merry go round when child reached the center ?

Answer 1

Answer on Question #74189, Physics / Mechanics — Relativity

Question a child of mass 50kg is standing an the edge of merry go round of mass 250kg and radius 3m which is rotating with an angular velocity of 30rad/sec. what will be the final angular velocity of the merry go round when child reached the center ?

Solution We need to use conservation of angular momentum here. Initially we have sum of moments of child and marry-go-around but in the end moment of child becomes 0. Hence:

$w_{1}(I_{c}+I_{d})=w_{2}I_{d}$

Here we have: $w_{1}=30$ rad/s - initial angular velocity, $I_{c}=m_{c}r_{d}^{2}$ is moment of inertia of a child and $I_{d}=m_{d}r_{d}^{2}/2$ is moment of inertia of marry-go-around, which we assumed is a disk, $m_{c}=50$ kg, $m_{d}=250$ kg, $r_{d}=3$ m. So we find final angular velocity:

$w_{2}=w_{1}\frac{m_{d}r_{d}^{2}/2}{m_{c}r_{d}^{2}+m_{d}r_{d}^{2}/2}=30\frac{1125}{450+1125}\approx 21.4\,rad/s$