Question

Consider a merry-go-round that has the form of a disc with radius 5.5 m and mass 155 kg. If five children, each of mass 20 kg, sit on the outer edge of the merry-go-round, what is the total moment of inertia?

Answer 1

Answer:

$I=5369.375$

Explanation:

Given:

• mass of merry go round, $M=155\ kg$

• radius of merry go round, $r=5.5\ m$

• mass of child, $m=20\ kg$

Considering merry-go-round as a disk, its moment of inertia is given as:

$I_d=\frac{1}{2} M.r^2$

$I_d=0.5\times 155\times 5.5^2$

$I_d=2344.375\ kg.m^2$

Considering children as point masses, their moment of inertia is given as:

$I_C=5(m.r^2)$

since there are 5 children

$I_C=5\times20\times 5.5^2$

$I_C=3025\ kg.m^2$

Now, total moment of inertia:

$I=I_C+I_d$

$I=3025+2344.375$

$I=5369.375$