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 $3Hz$ to $17 Hz$ in $5 s$ , what torque was applied to the object?

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Answer 1 · 2018-04-03T06:12:58

The torque was $=2586.2Nm$

The torque is the rate of change of angular momentum

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

For the object, $I=mr^2$

The mass is $m=3 kg$

The radius of the path is $r=7m$

So the moment of inertia is

, $I=3*(7)^2=147kgm^2$

The angular acceleration is

$alpha=(2pif_1-2pif_0)/t=(34-6)pi/5=28/5pirads^-2$

So,

The torque is

$tau=Ialpha=147*28/5pi=2586.2Nm$

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 3Hz 3Hz to 17 Hz 17 Hz in 5 s5 s, what torque was applied to the object?