Astudent sits at rest on a piano stool that can rotate without friction. the moment of inertia of the student-stool system is 4.4 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.

0.56191 rad/s

Explanation:

r = Distance at which the ball is caught = 0.45 m

m = Mass of ball = 2 kg

v = Velocity of ball = 3 m/s

= Moment of inertia of stool student system = 4.4 kgm²

Initial angular momentum is

As the stool rotates the linear momentum is not conserved but the angular momentum is conserved.

Final angular momentum is

Moment of inertia is given by

= Moment of inertia of ball

As the angular momentum of the system is conserved

The angular speed of the stool is 0.56191 rad/s

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:

asthenosphere and convection