An object with a mass of $3 k g$ $3 kg$ is traveling in a circular path of a radius of $3 m$ $3 m$ . If the object's angular velocity changes from $2 H z$ $2 Hz$ to $7 H z$ $7 Hz$ in $8 s$ $8 s$ , what torque was applied to the object?

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Answer 1 · 2016-12-25T07:42:38

The torque is $= 53.01 N m$ $=53.01Nm$

The torque is the rate of change of angular momentum

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

The moment of inertia is $I = \frac{1}{2} m r^{2}$ $I=1/2mr^2$

$= \frac{1}{2} \cdot 3 \cdot 3^{2} = \frac{27}{2} k g m^{2}$ $=1/2*3*3^2= 27/2 kgm^2$

The rate of change of angular velocity is

$\frac{d ω}{d t} = \frac{7 - 2}{8} \cdot 2 π$ $(domega)/dt=(7-2)/8*2pi$

$= \frac{5}{4} π r a d s^{- 2}$ $=5/4pi rads^(-2)$

So the torque is $τ = \frac{27}{2} \cdot \frac{5}{4} π N m = \frac{135}{8} π N m = 53.01 N m$ $tau=27/2*5/4pi Nm=135/8piNm=53.01Nm$

An object with a mass of 3kg 3 kg is traveling in a circular path of a radius of 3m3 m. If the object's angular velocity changes from 2Hz 2 Hz to 7Hz 7 Hz in 8s 8 s, what torque was applied to the object?