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 $2 Hz$ in $3 s$ , what torque was applied to the object?

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Answer 1 · 2016-12-25T06:22:57

The torque is $=513.1 Nm$

The torque is the rate of change of angular momentum

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

The is $I=1/2mr^2$

$=1/2*2*7^2= 49 kgm^2$

The rate of change of angular velocity is

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

$=10/3pi rads^(-2)$

So the torque is $tau=49*10/3pi Nm=490/3piNm=513.1Nm$

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 2 Hz 2 Hz in 3 s 3 s, what torque was applied to the object?