The rate of rotation of a solid disk with a radius of $8 m$ and mass of $5 kg$ constantly changes from $16 Hz$ to $5 Hz$ . If the change in rotational frequency occurs over $7 s$ , what torque was applied to the disk?

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Answer 1 · 2017-03-24T07:51:00

The torque was $=1579.8Nm$

The torque is the rate of change of angular momentum

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

The moment of inertia of a solid disc is

$I=1/2*mr^2$

$=1/2*5*8^2= 160 kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(16-5)/7*2pi$

$=(22/7pi) rads^(-2)$

So the torque is $tau=160*(22/7pi) Nm=1579.8Nm$

The rate of rotation of a solid disk with a radius of 8 m8 m and mass of 5 kg5 kg constantly changes from 16 Hz16 Hz to 5 Hz5 Hz. If the change in rotational frequency occurs over 7 s7 s, what torque was applied to the disk?