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 $2 H z$ $2 Hz$ to $12 H z$ $12 Hz$ in $2 s$ $2 s$ , what torque was applied to the object?

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Answer 1 · 2018-07-04T06:02:31

The torque is $= 1005.3 N m$ $=1005.3Nm$

The torque is the rate of change of angular momentum

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

For the object, the moment of inertia is

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

The mass of the object is $m = 2 k g$ $m=2 kg$

The radius of the circular path is $r = 4 m$ $r=4m$

The moment of inertia is

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

The angular acceleration is

$α = 2 π \frac{f_{2} - f_{1}}{t} = 2 π \frac{12 - 2}{2} = 10 π r a d s^{- 2}$ $alpha=2pi(f_2-f_1)/t=2pi(12-2)/2=10pirads^-2$

The torque is

$τ = I ω = 32 \cdot 10 π = 1005.3 N m$ $tau=I omega=32*10pi=1005.3Nm$

An object with a mass of 2kg 2 kg is traveling in a circular path of a radius of 4m4 m. If the object's angular velocity changes from 2Hz 2 Hz to 12Hz 12 Hz in 2s 2 s, what torque was applied to the object?