An object with a mass of $2 k g$ $2 kg$ is traveling in a circular path of a radius of $2 m$ $2 m$ . If the object's angular speed changes from $1 H z$ $1 Hz$ to $3 H z$ $3 Hz$ in $1 s$ $1 s$ , what torque was applied to the object?

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Answer 1 · 2017-03-07T18:00:49

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

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

$= 2 \cdot 2^{2} = 8 k g m^{2}$ $=2*2^2= 8 kgm^2$

The rate of change of angular velocity is

$\frac{d ω}{d t} = \frac{3 - 1}{1} \cdot 2 π$ $(domega)/dt=(3-1)/1*2pi$

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

So the torque is $τ = 8 \cdot (4 π) N m = 32 π N m = 100.5 N m$ $tau=8*(4pi) Nm=32piNm=100.5Nm$

An object with a mass of 2 kg2kg 2 kg is traveling in a circular path of a radius of 2 m2m2 m. If the object's angular speed changes from 1 Hz1Hz 1 Hz to 3 Hz3Hz 3 Hz in 1 s1s 1 s, what torque was applied to the object?