Aspinning wheel is slowed down by a brake, giving it a constant angular acceleration of ? 5.20 rad/s2. during a 3.80-s time interval, the wheel rotates through 70.4 rad. what is the angular speed of the wheel at the end of the 3.80-s interval

We can answer this using the rotational version of the kinematic equations:
θ = θ₀ + ω₀t + ½αt²     > 1

ω² = ω₀² + 2αθ            > 2

Where:

θ = final angular displacement = 70.4 rad

θ₀ = initial angular displacement = 0

ω₀ = initial angular speed

ω = final angular speed

t = time = 3.80 s

α = angular acceleration = -5.20 rad/s^2

Substituting the values into equation 1:
70.4 = 0 + ω₀(3.80) + ½(-5.20)(3.80)² 

ω₀ = (70.4 + 37.544) / 3.80 

ω₀ = 28.406 rad/s 

Using equation 2:
ω² = (28.406)² + 2(-5.2)70.4 

ω = 8.65 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: