An object with a mass of $3 k g$ $3 kg$ is traveling in a circular path of a radius of $7 m$ $7 m$ . If the object's angular velocity changes from $3 H z$ $3 Hz$ to $29 H z$ $29 Hz$ in $3 s$ $3 s$ , what torque was applied to the object?

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Answer 1 · 2016-03-04T13:06:59

Use the basics of rotation around a fixed axis. Remember to use $r a d s$ $rads$ for the angle.

$τ=2548π(kg*m^2)/s^2=8004,78(kg*m^2)/s^2$

The torque is equal to:

$τ=I*a_(θ)$

Where $I$ is the moment of inertia and $a_(θ)$ is the angular acceleration.

The moment of inertia:

$I=m*r^2$

$I=3kg*7^2m^2$

$I=147kg*m^2$

The angular acceleration:

$a_(θ)=(dω)/dt$

$a_(θ)=(d2πf)/dt$

$a_(θ)=2π(df)/dt$

$a_(θ)=2π(29-3)/3((rad)/s)/s$

$a_(θ)=52/3π(rad)/s^2$

Therefore:

$τ=147*52/3πkg*m^2*1/s^2$

$τ=2548π(kg*m^2)/s^2=8004,78(kg*m^2)/s^2$

An object with a mass of 3 kg3kg 3 kg is traveling in a circular path of a radius of 7 m7m7 m. If the object's angular velocity changes from 3 Hz3Hz 3 Hz to 29 Hz29Hz 29 Hz in 3 s3s3 s, what torque was applied to the object?