An object with a mass of $2 k g$ $2 kg$ is traveling in a circular path of a radius of $7 m$ $7 m$ . If the object's angular velocity changes from $7 H z$ $7 Hz$ to $9 H z$ $9 Hz$ in $3 s$ $3 s$ , what torque was applied to the object?

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Answer 1 · 2017-11-01T06:27:15

410.7 Nm

$Torque = Rate of change of Angular Momentum$ $"Torque = Rate of change of Angular Momentum"$

$= \frac{L_{f} - L_{i}}{t}$ $= (L_f - L_i) / t$

$= (I ω_f - I ω_i) / t$ ………[∵ Angular Momentum = $I ω$ ]

$= (I(ω_f - ω_i))/t$

$= (2piI(f_f - f_i))/t$ …………[ $∵ ω = 2pif$ ]

$=(2pixxmr^2(f_f - f_i))/t$

$=(2xx22/7 × 2kg × (7 m)^2 × (9Hz - 7Hz))/(3s)$

$=410.7$ Nm

An object with a mass of 2 kg2kg 2 kg is traveling in a circular path of a radius of 7 m7m7 m. If the object's angular velocity changes from 7 Hz7Hz 7 Hz to 9 Hz9Hz 9 Hz in 3 s3s 3 s, what torque was applied to the object?