Consider a merry-go-round that has the form of a disc with radius 5.6 m and mass 140 kg. If two children, each of mass 20 kg, sit on the outer edge of the merry-go-round, what is the total moment of inertia

3449.6 kgm²

Explanation:

Given that

Radius of the merry go round, r = 5.6 m

Mass of the merry go round, M = 140 kg

Mass of the children, m = 40 kg

Total moment of inertia, I = ?

The total moment of inertia is given as the sum of moments of inertia of the merry-go-round in addition to that of the child. Mathematically, we say

I = 1/2Mr² + mr²

I = 1/2 * 140 * 5.6² + 40 * 5.6²

I = 70 * 31.36 + 40 * 31.36

I = 2195.2 + 1254.4

I = 3449.6 kgm²

Therefore, the total moment of inertia of the merry go round and that of the children on it is 3449.6 kgm²

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .