An object with a mass of $2 kg$ is traveling in a circular path of a radius of $4 m$ . If the object's angular velocity changes from $4 Hz$ to $12 Hz$ in $3 s$ , what torque was applied to the object?

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Answer 1 · 2017-04-10T09:06:57

The torque was $=536.2Nm$

The torque is the rate of change of angular momentum

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

For the object, the moment of inertia is

$I=(mr^2)$

So, $I=2*(4)^2=32kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(12-4)/3*2pi$

$=(16/3pi) rads^(-2)$

So the torque is $tau=32*(16/3pi) N=536.2Nm$

An object with a mass of 2 kg 2 kg is traveling in a circular path of a radius of 4 m4 m. If the object's angular velocity changes from 4 Hz 4 Hz to 12 Hz 12 Hz in 3 s 3 s, what torque was applied to the object?