An object with a mass of $3 kg$ is traveling in a circular path of a radius of $5 m$ . If the object's angular velocity changes from $1 Hz$ to $8 Hz$ in $5 s$ , what torque was applied to the object?

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Answer 1 · 2017-02-06T06:44:17

The torque was $=329.9Nm$

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 $I=mr^2$

$=3*5^2= 75 kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(8-1)/5*2pi$

$=((7pi)/5) rads^(-2)$

So the torque is $tau=75*(7pi)/5 Nm=105piNm=329.9Nm$

An object with a mass of 3 kg 3 kg is traveling in a circular path of a radius of 5 m5 m. If the object's angular velocity changes from 1 Hz 1 Hz to 8 Hz 8 Hz in 5 s 5 s, what torque was applied to the object?