An object with a mass of $2 kg$ is traveling in a circular path of a radius of $2 m$ . If the object's angular velocity changes from $1 Hz$ to $6 Hz$ in $1 s$ , what torque was applied to the object?

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Answer 1 · 2017-05-21T17:21:59

The torque was $=251.3Nm$

The torque is the rate of change of angular momentum

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

For the object, $I=mr^2$

$I=2*2^2=8kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(6-1)/1*2pi$

$=(10pi) rads^(-2)$

So the torque is $tau=8*(10pi) Nm=80piNm=251.3Nm$

An object with a mass of 2 kg 2 kg is traveling in a circular path of a radius of 2 m2 m. If the object's angular velocity changes from 1 Hz 1 Hz to 6 Hz 6 Hz in 1 s 1 s, what torque was applied to the object?