An object with a mass of $3 kg$ is traveling in a circular path of a radius of $5 m$ . If the object's angular velocity changes from $7 Hz$ to $8 Hz$ in $5 s$ , what torque was applied to the object?

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Answer 1 · 2017-11-16T19:02:32

The torque is $=157.1Nm$

The torque is the rate of change of angular momentum

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

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

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

For the object, $I=mr^2$

So, $I=3*(5)^2=75kgm^2$

And the rate of change of angular velocity is

$(d omega)/dt=(Deltaomega)/t=(2pif_1-2pif_2)/t$

$=(16pi-14pi)/5=(2/5pi)rads^-2$

So,

The torque is

$tau=75*2/5pi=157.1Nm$

An object with a mass of 3 kg 3 kg is traveling in a circular path of a radius of 5 m5 m. If the object's angular velocity changes from 7 Hz 7 Hz to 8 Hz 8 Hz in 5 s 5 s, what torque was applied to the object?