Rotational dynamics about a fixed axis: A solid uniform sphere of mass 1.85 kg and diameter 45.0 cm spins about an axle through its center. Starting with an angular velocity of 2.40 rev/s, it stops after turning through 18.2 rev with uniform acceleration. The net torque acting on this sphere as it is slowing down is closest to:A) 0.149 N m. B) 0.0620N m. C) 0.00593 N m. D) 0.0372 N m. E) 0.0466 N·m

(D) The net torque acting on this sphere as it is slowing down is closest to  0.0372 N.m

Explanation:

Given;

mass of the solid sphere, m =  1.85 kg

radius of the sphere, r = ¹/₂ of diameter = 22.5 cm

initial angular velocity, ω = 2.40 rev/s = 15.08 rad/s

angular revolution, θ = 18.2 rev = 114.37 rad

Torque on the sphere, τ = Iα

Where;

I is moment of inertia

α is angular acceleration

Angular acceleration is calculated as;

moment of inertia of solid sphere, I = ²/₅mr²

                                                           = ²/₅(1.85)(0.225)²

                                                           = 0.03746 kg.m²

Finally, the net torque on the sphere is calculated as;

τ = Iα

τ = 0.03746 x 0.994

τ = 0.0372 N.m

Therefore, the net torque acting on this sphere as it is slowing down is closest to  0.0372 N.m

b.

explanation:

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