A sphere of mass 2kg and radius 5cm is rotating at the rate of 300 revolutions per minute. Calculate the torque required to stop it in 6.28 revolutions. [Moment of inertia of sphere about diameter = 2/5 mass * (radius)^2]
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Torque = Rate of change of angular momentum
T = dL / dt
= I × (ωf - ωi) / t ………[Here I = Moment of inertia]
= -[(2/5) × mR² × ωi] / t …………[∵ ωf = 0]
= -[2/5 × 2 kg × (0.05 m)² × (300/60) × 2 π rad/s] / 6.28 s
= -0.01 N.m
Magnitude of torque required to stop the sphere rotating is 0.01 N.m
T = dL / dt
= I × (ωf - ωi) / t ………[Here I = Moment of inertia]
= -[(2/5) × mR² × ωi] / t …………[∵ ωf = 0]
= -[2/5 × 2 kg × (0.05 m)² × (300/60) × 2 π rad/s] / 6.28 s
= -0.01 N.m
Magnitude of torque required to stop the sphere rotating is 0.01 N.m
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