An object with a mass of $2 kg$ is traveling in a circular path of a radius of $2 m$ . If the object's angular velocity changes from $2 Hz$ to $16 Hz$ in $1 s$ , what torque was applied to the object?

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Answer 1 · 2017-02-13T06:57:42

The torque was $=703.7Nm$

The torque is the rate of change of angular momentum

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

The moment of inertia of the object is $I=mr^2$

$=2*2^2= 8 kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(16-2)/1*2pi$

$=((28pi) rads^(-2)$

So the torque is $tau=8*(28pi) Nm=224piNm=703.7Nm$

An object with a mass of 2 kg 2 kg is traveling in a circular path of a radius of 2 m2 m. If the object's angular velocity changes from 2 Hz 2 Hz to 16 Hz 16 Hz in 1 s 1 s, what torque was applied to the object?