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. 0.037 N m.

Explanation:

Given:

Diameter, d = 45 cm

Radius, r = d/2

= 0.225 m

Mass, m = 1.85 kg

Initial velocity, wi = 2.4 rev/s

θ = 18.2 rev

Final velocity, wf = 0 rev/s

Inertia of a uniform sphere, I = 2/5 × m × R^2

= 2/5 × 1.85 × 0.225^2

= 0.0375 kg.m^2

Using equation of angular motion,

wf^2 = wi^2 + 2ao × θ

Where,

ao = angular acceleration

ao = (2.4^2)/2 × 18.2

= 0.158 rev/s^2

Converting from rev/s^2 to rad/s^2,

0.158 rev/s^2 × 2pi rad/1 rev

= 0.993 rad/s^2

Torque, t = I × ao

= 0.0375 × 0.993

= 0.037 Nm

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