An object with a mass of $8 kg$ is traveling in a circular path of a radius of $9 m$ . If the object's angular velocity changes from $4 Hz$ to $6 Hz$ in $8 s$ , what torque was applied to the object?

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Answer 1 · 2017-04-19T09:32:00

The torque was $=1017.9Nm$

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, $I=8*(9)^2=648kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(6-4)/8*2pi$

$=(1/2pi) rads^(-2)$

So the torque is $tau=648*(1/2pi) Nm=1017.9Nm$

An object with a mass of 8 kg 8 kg is traveling in a circular path of a radius of 9 m9 m. If the object's angular velocity changes from 4 Hz 4 Hz to 6 Hz 6 Hz in 8 s 8 s, what torque was applied to the object?