An object with a mass of $2 kg$ is traveling in a circular path of a radius of $2 m$ . If the object's angular velocity changes from $1 Hz$ to $4 Hz$ in $1 s$ , what torque was applied to the object?

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Answer 1 · 2016-12-25T08:00:10

The torque is $=75.4Nm$

The torque is the rate of change of angular momentum

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

The is $I=1/2mr^2$

$=1/2*2*2^2= 4 kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(4-1)/1*2pi$

$=6pi rads^(-2)$

So the torque is $tau=4*6pi Nm=24piNm=75.4Nm$

An object with a mass of 2 kg 2 kg is traveling in a circular path of a radius of 2 m2 m. If the object's angular velocity changes from 1 Hz 1 Hz to 4 Hz 4 Hz in 1 s 1 s, what torque was applied to the object?