The rate of rotation of a solid disk with a radius of $5 m$ and mass of $5 kg$ constantly changes from $18 Hz$ to $24 Hz$ . If the change in rotational frequency occurs over $1 s$ , what torque was applied to the disk?

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Answer 1 · 2017-06-08T05:07:22

The torque was $=2356.2Nm$

The torque is the rate of change of angular momentum

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

Where the moment of inertiais $=I$

and $omega$ is the angular velocity

The mass of the disc is $m=5kg$

The radius of the disc is $r=5m$

For the solid disc, $I=(1/2mr^2)$

So, $I=1/2*5*(5)^2=125/2kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(24-18)/1*2pi$

$=(12pi) rads^(-2)$

So the torque is $tau=125/2*(12pi) Nm=2356.2Nm$

The rate of rotation of a solid disk with a radius of 5 m5 m and mass of 5 kg5 kg constantly changes from 18 Hz18 Hz to 24 Hz24 Hz. If the change in rotational frequency occurs over 1 s1 s, what torque was applied to the disk?