What torque would have to be applied to a rod with a length of $1 m$ and a mass of $1 kg$ to change its horizontal spin by a frequency of $2 Hz$ over $2 s$ ?

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Answer 1 · 2017-03-03T11:04:33

The torque(for the rod rotating about the center) is $=0.52Nm$
The torque (for the rod rotating about one end) is $=2.1Nm$

The torque is the rate of change of angular momentum

$tau=(dL)/dt=(d(Iomega))/dt=I(domega)/dt$

The moment of inertia of a rod, rotating about the center is

$I=1/12*mL^2$

$=1/12*1*1^2= 1/12 kgm^2$

The rate of change of angular velocity is

$(domega)/dt=(2)/2*2pi$

$=(2pi) rads^(-2)$

So the torque is $tau=1/12*(2pi) Nm=1/6piNm=0.52Nm$

The moment of inertia of a rod, rotating about one end is

$I=1/3*mL^2$

$=1/3*1*1^2=1/3kgm^2$

So,

The torque is $tau=1/3*(2pi)=2/3pi=2.1Nm$

What torque would have to be applied to a rod with a length of 1 m1 m and a mass of 1 kg1 kg to change its horizontal spin by a frequency of 2 Hz2 Hz over 2 s2 s?