Two wheels have the same mass and radius of 4.2 kg and 0.42 m, respectively. One has (a) the shape of a hoop and the other (b) the shape of a solid disk. The wheels start from rest and have a constant angular acceleration with respect to a rotational axis that is perpendicular to the plane of the wheel at its center. Each turns through an angle of 14 rad in 8.3 s. Find the net external torque that acts on each wheel.

τsolid = 0.15 N•m

τhoop = 0.30 N•m

Explanation:

θ = ½αt²

α = 2θ/t² = 2(14)/8.3² = 0.406445 rad/s²

Solid disk I = ½mr² = ½(4.2)0.42² = 0.37044 kg•m²

τ = Iα = 0.37044(0.406445) = 0.150563... N•m

Hoop disk I = mr² = (4.2)0.42² = 0.74088 kg•m²

τ = Iα = 0.74088(0.406445) = 0.301127... N•m

second mirror gathers light from a faraway object and reflects it to another mirror. - a.

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: