An object with a mass of $7 kg$ is traveling in a circular path of a radius of $9 m$ . If the object's angular velocity changes from $5 Hz$ to $3 Hz$ in $8 s$ , what torque was applied to the object?

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Answer 1 · 2017-06-26T15:47:51

The torque was $=890.6Nm$

The torque is the rate of change of angular momentum

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

For a the object, $I=mr^2$

So, $I=7*(9)^2=567kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(5-3)/8*2pi$

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

So the torque is $tau=567*(1/2pi) Nm=890.6Nm$

An object with a mass of 7 kg 7 kg is traveling in a circular path of a radius of 9 m9 m. If the object's angular velocity changes from 5 Hz 5 Hz to 3 Hz 3 Hz in 8 s 8 s, what torque was applied to the object?