Astudent sits at rest on a piano stool that can rotate without friction. the moment of inertia of the student-stool system is 4.5 kg⋅m2 . a second student tosses a 2.0 kg mass with a speed of 3.0 m/s to the student on the stool, who catches it at a distance of 0.45 m from the axis of rotation. what is the resulting angular speed of thestudent and the stool?

   w = 0.55 rad / s

Explanation:

For this exercise let's use the conservation of angular momentum, let's write the moment in two moments

Initial

    L₀ = r p + 0

    L₀ = r mv

The first term is the angular momentum of the mass

Final

      Lf = (I + m r²) w

Where I is the moment of inertia of the stool and the other term is the moment of inertia of the mass

      L₀ = Lf

      r mv = (I + m r²) w

      w = m r v / (I + m r²)

Let's calculate

      w = 2.0 0.45 3.0 / (4.5 + 2.0 0.45²)

      w = 2.7 / 4.9

     w = 0.55 rad / s

tube or goog with be a great resource to with that question

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: