An object with a mass of $3 kg$ is traveling in a circular path of a radius of $9 m$ . If the object's angular velocity changes from $9 Hz$ to $14 Hz$ in $8 s$ , what torque was applied to the object?

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Answer 1 · 2018-03-15T18:02:03

The torque is $=954.3Nm$

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 $r=9m$

So the moment of inertia is

, $I=3*(9)^2=243kgm^2$

The angular acceleration is

$alpha=(2pif_1-2pif_0)/t=(28-18)pi/8=5/4pirads^-2$

So,

The torque is

$tau=Ialpha=243*5/4pi=954.3Nm$

An object with a mass of 3 kg 3 kg is traveling in a circular path of a radius of 9 m9 m. If the object's angular velocity changes from 9 Hz 9 Hz to 14 Hz 14 Hz in 8 s 8 s, what torque was applied to the object?