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 $3 Hz$ to $9 Hz$ in $1 s$ , what torque was applied to the object?

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Answer 1 · 2016-04-15T09:39:32

$96pi Nm$

Comparing linear motion and Rotational motion for understanding

For Linear motion $--$ For rotational motion,

mass $->$ moment of Inertial

Force $->$ Torque

velocity $->$ Angular velocity

acceleration $->$ ANgular acceleration

So,

$F= ma$ $->$ $->$ $tau = I alpha$

Here,

$alpha = (omega _2 -omega _1)/(Delta t) =(2pixxn_2-2pixxn_1)/(Deltat)=(2pi)xx( (9-3))/1 s^(-2) = 12pis^(-2)$

and
$I = mr^2 = 2kg*2^2 m^2 = 8 kgm^2$

So $tau = 8 kgm^2 * 12pis^(-2) = 96pi Nm$

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 3 Hz 3 Hz to 9 Hz 9 Hz in 1 s 1 s, what torque was applied to the object?