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

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Answer 1 · 2017-07-17T22:24:26

We will use cassical mechanics (rotation) equations to solve this problem.

With frequency of $3Hz$ the velocity is $ω_1=2pif_1=6pi(rads)/s$

With frequency of $7Hz$ the velocity is $ω_2=2pif_2=14pi(rads)/s$

The angular acceleration is then

$α=(Δω)/(Δt)=(14pi-6pi)/3=(8pi)/3(rads)/s^2$

and the torque is :

$Τ=Iα=mr^2α=3*49*(8pi)/3=392piNm$

An object with a mass of 3 kg 3 kg is traveling in a circular path of a radius of 7 m7 m. If the object's angular velocity changes from 3 Hz 3 Hz to 7 Hz 7 Hz in 3 s3 s, what torque was applied to the object?