An object with a mass of $2 kg$ is traveling in a circular path of a radius of $7 m$ . If the object's angular velocity changes from $7 Hz$ to $8 Hz$ in $3 s$ , what torque was applied to the object?

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Answer 1 · 2017-04-29T07:24:03

The torque is $=205.3Nm$

The torque is the rate of change of angular momentum

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

The moment of inertiai is $=I$

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

So, $I=2*(7)^2=98kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(8-7)/3*2pi$

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

So the torque is $tau=98*(2/3pi) Nm=205.3Nm$

An object with a mass of 2 kg 2 kg is traveling in a circular path of a radius of 7 m7 m. If the object's angular velocity changes from 7 Hz 7 Hz to 8 Hz 8 Hz in 3 s 3 s, what torque was applied to the object?