An object with a mass of $8 k g$ $8 kg$ is traveling in a circular path of a radius of $12 m$ $12 m$ . If the object's angular velocity changes from $5 H z$ $5 Hz$ to $7 H z$ $7 Hz$ in $6 s$ $6 s$ , what torque was applied to the object?

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Answer 1 · 2017-11-11T06:44:48

The torque is $= 2412.7 N m$ $=2412.7Nm$

The torque is the rate of change of angular momentum

$τ = \frac{d L}{d t} = \frac{d (I ω)}{d t} = I \frac{d ω}{d t}$ $tau=(dL)/dt=(d(Iomega))/dt=I(domega)/dt$

where $I$ $I$ is the moment of inertia

The mass of the object is $m = 8 k g$ $m=8kg$

The radius of the path is $r = 12 m$ $r=12m$

For the object, $I = m r^{2}$ $I=mr^2$

So, $I = 8 \cdot {(12)}^{2} = 1152 k g m^{2}$ $I=8*(12)^2=1152kgm^2$

And the rate of change of angular velocity is

$(d omega)/dt=(Deltaomega)/t=(2pif_1-2pif_2)/t$

$=(14pi-10pi)/6=(2/3pi)rads^-2$

So,

The torque is

$tau=1152*2/3pi=2412.7Nm$

An object with a mass of 8 kg8kg 8 kg is traveling in a circular path of a radius of 12 m12m12 m. If the object's angular velocity changes from 5 Hz5Hz 5 Hz to 7 Hz7Hz 7 Hz in 6 s6s 6 s, what torque was applied to the object?