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

b

explanation:

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: