An object with a mass of $2 k g$ $2 kg$ is traveling in a circular path of a radius of $4 m$ $4 m$ . If the object's angular velocity changes from $3 H z$ $3 Hz$ to $4 H z$ $4 Hz$ in $2 s$ $2 s$ , what torque was applied to the object?

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Answer 1 · 2017-01-31T10:14:18

The torque was $= 100.5 N m$ $=100.5Nm$

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 $I = m r^{2}$ $I=mr^2$

$= 2 \cdot 4^{2} = 32 k g m^{2}$ $=2*4^2= 32 kgm^2$

The rate of change of angular velocity is

$\frac{d ω}{d t} = \frac{4 - 3}{2} \cdot 2 π$ $(domega)/dt=(4-3)/2*2pi$

$= π r a d s^{- 2}$ $=pi rads^(-2)$

So the torque is $τ = 32 \cdot π N m = 100.5 N m$ $tau=32*pi Nm=100.5Nm$

An object with a mass of 2 kg2kg 2 kg is traveling in a circular path of a radius of 4 m4m4 m. If the object's angular velocity changes from 3 Hz3Hz 3 Hz to 4 Hz4Hz 4 Hz in 2 s2s 2 s, what torque was applied to the object?