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

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Answer 1 · 2016-12-25T07:42:38

The torque is $=53.01Nm$

The torque is the rate of change of angular momentum

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

The moment of inertia is $I=1/2mr^2$

$=1/2*3*3^2= 27/2 kgm^2$

The rate of change of angular velocity is

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

$=5/4pi rads^(-2)$

So the torque is $tau=27/2*5/4pi Nm=135/8piNm=53.01Nm$

An object with a mass of 3 kg 3 kg is traveling in a circular path of a radius of 3 m3 m. If the object's angular velocity changes from 2 Hz 2 Hz to 7 Hz 7 Hz in 8 s 8 s, what torque was applied to the object?