Consider four objects, each having the same mass and the same radius:

1. a solid sphere
2. a hollow sphere
3. a flat disk in the x, y plane
4. a hoop in the x, y plane
The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is:

1. Solid Sphere: 0.4 kg m²

2. Flat Disk in x,y plane: 0.5 kg m²

3. A Hollow Sphere: 0.67 kg m²

4. Hoop in x,y plane: 1 kg m²

Explanation:

The formulae for the rotation inertia of given shapes about z-axis are given as follows:

1. Solid Sphere: (2/5)(MR²)

2. A Hollow Sphere: (2/3)(MR²)

3. Flat Disk in x,y plane = (1/2)(MR²)

4. Hoop in the x,y plane = MR²

where,

M = mass

R = Radius

Since, it is stated that all shapes have same mass and radius. Therefore, we assume a mass of 1 kg and radius of 1 m for each shape. Hence values become:

1. Solid Sphere: (2/5)(1 kg)(1 m)²

2. A Hollow Sphere: (2/3)(1 kg)(1 m)²

3. Flat Disk in x,y plane = (1/2)(1 kg)(1 m)²

4. Hoop in the x,y plane = (1 kg)(1 m)²

Solving the values, we get:

1. Solid Sphere: 0.4 kg m²

2. A Hollow Sphere: 0.67 kg m²

3. Flat Disk in x,y plane = 0.5 kg m²

4. Hoop in the x,y plane = 1 kg m²

Therefore, it is clear from above calculations, that the order of increasing of rotational inertia of these shapes will be as follows:

1. Solid Sphere: 0.4 kg m²

2. Flat Disk in x,y plane: 0.5 kg m²

3. A Hollow Sphere: 0.67 kg m²

4. Hoop in x,y plane: 1 kg m²

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: