An object with a mass of $8 kg$ is traveling in a circular path of a radius of $12 m$ . If the object's angular velocity changes from $15 Hz$ to $6 Hz$ in $6 s$ , what torque was applied to the object?

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Answer 1 · 2017-01-25T09:10:28

The answer is $=10857.3Nm$

The torque is the rate of change of angular momentum

$tau=(dL)/dt=(d(Iomega))/dt=I(domega)/dt$

The moment of inertia of the object is $I=mr^2$

$=8*12^2= 1152 kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(15-6)/6*2pi$

$=((18pi)/6)=3pi rads^(-2)$

So the torque is $tau=1152*(3pi) Nm=3456piNm=10857.3Nm$

An object with a mass of 8 kg 8 kg is traveling in a circular path of a radius of 12 m12 m. If the object's angular velocity changes from 15 Hz 15 Hz to 6 Hz 6 Hz in 6 s 6 s, what torque was applied to the object?