An object with a mass of $3 k g$ $3 kg$ 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 $4 H z$ $4 Hz$ in $5 s$ $5 s$ , what torque was applied to the object?

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Answer 1 · 2017-01-12T08:31:31

The torque is $= 542.9 N m$ $=542.9Nm$

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 of the object is $I = m r^{2}$ $I=mr^2$

$= 3 \cdot 12^{2} = 432 k g m^{2}$ $=3*12^2= 432 kgm^2$

The rate of change of angular velocity is

$\frac{d ω}{d t} = \frac{5 - 4}{5} \cdot 2 π$ $(domega)/dt=(5-4)/5*2pi$

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

So the torque is $τ = 432 \cdot \frac{2 π}{5} N m = \frac{864}{5} π N m = 542.9 N m$ $tau=432*(2pi)/5 Nm=864/5piNm=542.9Nm$

An object with a mass of 3kg 3 kg is traveling in a circular path of a radius of 12m12 m. If the object's angular velocity changes from 5Hz 5 Hz to 4Hz 4 Hz in 5s 5 s, what torque was applied to the object?