Question #92227

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Answer 1 · 2017-03-21T10:23:58

The torque is $= 18816 N m$ $=18816Nm$

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 a circular disc is

$I = \frac{1}{2} \cdot m r^{2}$ $I=1/2*mr^2$

$= \frac{1}{2} \cdot 2800 \cdot 28^{2} = 1097600 k g m^{2}$ $=1/2*2800*28^2= 1097600 kgm^2$

The rate of change of angular velocity is

$\frac{d ω}{d t} = \frac{0.24}{14} = 0.0171 r a d s^{- 2}$ $(domega)/dt=0.24/14=0.0171rads^-2$

So the torque is $τ = 1097600 \cdot (0.0171) N m = 18816 N m$ $tau=1097600*(0.0171) Nm=18816Nm$