An object with a mass of $3 kg$ is traveling in a circular path of a radius of $7 m$ . If the object's angular velocity changes from $14 Hz$ to $23 Hz$ in $5 s$ , what torque was applied to the object?

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Answer 1 · 2017-04-14T07:34:29

The torque was $=1662.5Nm$

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

$I=mr^2$

$=3*7^2= 147 kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(23-14)/5*2pi$

$=(18/5pi) rads^(-2)$

So the torque is $tau=147*(18/5pi) Nm=1662.5Nm$

An object with a mass of 3 kg 3 kg is traveling in a circular path of a radius of 7 m7 m. If the object's angular velocity changes from 14 Hz 14 Hz to 23 Hz 23 Hz in 5 s5 s, what torque was applied to the object?