Question

A 30-kg child starts at the center of a playground merry-go-round that has a radius of 2.1 m and rotational inertia of 500 kg⋅m2 and walks out to the edge. The merry-go-round has a rotational speed of 0.20 s−1 when she is at the center?

Answer 1

`\omega = 0.16 s^(-1)`

Step-by-step explanation:

As we know that there is no torque on the system of merry go round

so the angular momentum will remain conserved

so here we have

`I_1\omega_0 = (I_1 + I_2)\omega`

so we will have

`I_1 = 500 kg m^2`

`I_2 = 30(2.1^2)`

`I_2 = 132.3 kg m^2`

`\omega_0 = 0.20 s^(-1)`

now from above formula

`500(0.20) = (500 + 132.3)\omega`

`\omega = 0.16 s^(-1)`