An object with a mass of $8 kg$ is traveling in a circular path of a radius of $12 m$ . If the object's angular velocity changes from $15 Hz$ to $4 Hz$ in $5 s$ , what torque was applied to the object?

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Answer 1 · 2017-09-19T11:42:37

The torque was $=15924.1Nm$

The torque is the rate of change of angular momentum

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

The mass of the object is $m=8kg$

The radius is $r=12m$

For the object, $I=mr^2$

So, $I=8*(12)^2=1152kgm^2$

And the rate of change of angular velocity is

$(d omega)/dt=(Deltaomega)/t=(30pi-8pi)/5=22/5pirads^-2$

So,

The torque is

$tau=1152*22/5pi=15924.1Nm$

An object with a mass of 8 kg 8 kg is traveling in a circular path of a radius of 12 m12 m. If the object's angular velocity changes from 15 Hz 15 Hz to 4 Hz 4 Hz in 5 s 5 s, what torque was applied to the object?