An object with a mass of $2 kg$ is traveling in a circular path of a radius of $7 m$ . 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 · 2018-02-23T07:00:11

The torque is $=123.2Nm$

The torque is the rate of change of angular momentum

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

For the object, $I=mr^2$

The mass is $m=2 kg$

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

So the moment of inertia is

, $I=2*(7)^2=98kgm^2$

The angular acceleration is

$alpha=(2pif_1-2pif_0)/t=(16-14)pi/5=1.257rads^-2$

So,

The torque is

$tau=Ialpha=98*1.257=123.2Nm$

An object with a mass of 2 kg 2 kg is traveling in a circular path of a radius of 7 m7 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?