An object with a mass of $3 kg$ is traveling in a circular path of a radius of $7 m$ . If the object's angular velocity changes from $6 Hz$ to $7 Hz$ in $3 s$ , what torque was applied to the object?

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Answer 1 · 2017-04-25T16:27:52

The torque was $=307.9Nm$

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, $I=(3*(7)^2)=147kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(7-6)/3*2pi$

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

So the torque is $tau=147*(2/3pi) Nm=307.9Nm$

An object with a mass of 3 kg 3 kg is traveling in a circular path of a radius of 7 m7 m. If the object's angular velocity changes from 6 Hz 6 Hz to 7 Hz 7 Hz in 3 s3 s, what torque was applied to the object?