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 $6 Hz$ to $9 Hz$ in $8 s$ , what torque was applied to the object?

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Answer 1 · 2018-06-04T12:53:39

The torque is $=21.21Nm$

The torque is the rate of change of angular momentum

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

For the object moving in a circular motion, $I=(mr^2)/2$

The mass is $m= 3kg$

The radius is $r=7m$

So, $I=3*(7)^2/2=73.5kgm^2$

The rate of change of angular velocity is

$alpha=(domega)/dt=(9-6)/8*2pi$

$=(3/4pi) rads^(-2)$

So the torque is $tau=9*(3/4pi) Nm=21.21Nm$

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 6 Hz 6 Hz to 9 Hz 9 Hz in 8 s 8 s, what torque was applied to the object?