An object with a mass of $3 kg$ is traveling in a circular path of a radius of $9 m$ . If the object's angular velocity changes from $2 Hz$ to $6 Hz$ in $8 s$ , what torque was applied to the object?

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Answer 1 · 2017-04-24T05:37:26

The torque was $=763.4Nm$

The torque is the rate of change of angular momentum

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

For the object, $I=(mr^2)$

So, $I=(3*(9)^2)=243kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(6-2)/8*2pi$

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

So the torque is $tau=243*(pi) Nm=763.4Nm$

An object with a mass of 3 kg 3 kg is traveling in a circular path of a radius of 9 m9 m. If the object's angular velocity changes from 2 Hz 2 Hz to 6 Hz 6 Hz in 8 s 8 s, what torque was applied to the object?