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.

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Answer:τsolid =0.15 N•mτhoop =0.30 N•mExplanation: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