As you may know, the key concept to use to solve this question is conservation of angular momentum. This concept is the argument that angular momentum is conserved unless non-zero net external torque is applied. In this question, as the child is simply walking towards the center, there is no net external torque applied in this situation. Hence, we can use conservation of angular momentum. Here is how the calculations would work:
Variables:
Li = initial angular momentum
Lf = final angular momentum
Ici = initial moment of inertia of a child
Icf = final moment of inertia of a child
Im = moment of inertia of a merry-go-round
Mc = mass of a child
Ri = initial distance between the child and center of a merry-go-round
Rf = final distance between the child and center of a merry-go-round
Hi,
Thank you for your question.
As you may know, the key concept to use to solve this question is conservation of angular momentum. This concept is the argument that angular momentum is conserved unless non-zero net external torque is applied. In this question, as the child is simply walking towards the center, there is no net external torque applied in this situation. Hence, we can use conservation of angular momentum. Here is how the calculations would work:
Variables:
Li = initial angular momentum
Lf = final angular momentum
Ici = initial moment of inertia of a child
Icf = final moment of inertia of a child
Im = moment of inertia of a merry-go-round
Mc = mass of a child
Ri = initial distance between the child and center of a merry-go-round
Rf = final distance between the child and center of a merry-go-round
ωi = initial angular velocity
ωf = final angular velocity
∑Li = ∑Lf
Ici*ωi + Im*ωi = Icf*ωf + Im*ωf
(Mc*(Ri)^2)*ωi + 102.021*ωi = (Mc*(Rf)^2)*ωf + 102.021*ωf
(49.2*(1.6)^2)*2.4 + 102.021*2.4 = (49.2*(0.608)^2 + 102.021)*ωf
ωf = 4.55155286 rad/s
Therefore, the answer to this question would be 4.55155286 rad/s.
Does this answer your question?