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 $13Hz$ to $17 Hz$ in $5 s$ , what torque was applied to the object?

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Answer 1 · 2018-06-27T14:17:32

The torque was $=738.9Nm$

The torque is the rate of change of angular momentum

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

For the object, the moment of inertia is

$I=mr^2$

The mass of the disc is $m=3 kg$

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

The moment of inertia is

$I=3*7^2=147kg m^2$

The angular acceleration is

$alpha=2pi(f_2-f_1)/t=2pi(17-13)/5=1.6pirads^-2$

The torque is

$tau=I omega=147*1.6pi=738.9Nm$

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 13Hz 13Hz to 17 Hz 17 Hz in 5 s5 s, what torque was applied to the object?