Determine the moment of inertia for three children weighing 64.0 lb, 44.0 lb and 83 lb sitting at different points on the edge of a rotating merry-go-round, which has a radius of 12 ft.
To determine the moment of inertia for the children sitting at different points on the merry-go-round, we need to calculate the moment of inertia for each child individually and then add them up.
The moment of inertia is calculated using the following formula:
I = m * r^2
where:
I is the moment of inertia,
m is the mass of the object, and
r is the distance from the axis of rotation.
First, let's calculate the moment of inertia for each child:
Child 1:
Mass (m1) = 64.0 lb
Distance from the axis of rotation (r1) = 12 ft
I1 = m1 * r1^2 = 64.0 lb * (12 ft)^2
Child 2:
Mass (m2) = 44.0 lb
Distance from the axis of rotation (r2) = 12 ft
I2 = m2 * r2^2 = 44.0 lb * (12 ft)^2
Child 3:
Mass (m3) = 83 lb
Distance from the axis of rotation (r3) = 12 ft
I3 = m3 * r3^2 = 83 lb * (12 ft)^2
Now, let's calculate the total moment of inertia by adding up the individual moments of inertia:
Total moment of inertia (Itotal) = I1 + I2 + I3
Calculate the values for I1, I2, and I3 using the given masses and distances, and then add them up to find the total moment of inertia.