An object with a mass of $3 kg$ is traveling in a circular path of a radius of $15 m$ . If the object's angular velocity changes from $25 Hz$ to $34 Hz$ in $9 s$ , what torque was applied to the object?

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Answer 1 · 2017-01-10T07:09:44

The torque is $=4241.2Nm$

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 mass is $I=mr^2$

$=3*15^2= 675 kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(34-25)/9*2pi$

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

So the torque is $tau=675*(2pi) Nm=1350piNm=4241.2Nm$

An object with a mass of 3 kg 3 kg is traveling in a circular path of a radius of 15 m15 m. If the object's angular velocity changes from 25 Hz 25 Hz to 34 Hz 34 Hz in 9 s9 s, what torque was applied to the object?