What torque would have to be applied to a rod with a length of $4 m$ $4 m$ and a mass of $8 k g$ $8 kg$ to change its horizontal spin by a frequency $9 H z$ $9 Hz$ over $2 s$ $2 s$ ?

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What torque would have to be applied to a rod with a length of $4 m$ $4 m$ and a mass of $8 k g$ $8 kg$ to change its horizontal spin by a frequency $9 H z$ $9 Hz$ over $2 s$ $2 s$ ?

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Answer 1 · 2018-01-11T14:30:03

The torque for the rod rotating about the center is $= 301.6 N m$ $=301.6Nm$
The torque for the rod rotating about one end is $= 1206.4 N m$ $=1206.4Nm$

Explanation:

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 mass of the rod is $m = 8 k g$ $m=8kg$

The length of the rod is $L = 4 m$ $L=4m$

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

$I = \frac{1}{12} \cdot m L^{2}$ $I=1/12*mL^2$

$= \frac{1}{12} \cdot 8 \cdot 4^{2} = 10.67 k g m^{2}$ $=1/12*8*4^2= 10.67 kgm^2$

The rate of change of angular velocity is

$\frac{d ω}{d t} = \frac{9}{2} \cdot 2 π$ $(domega)/dt=(9)/2*2pi$

$= (9 π) r a d s^{- 2}$ $=(9pi) rads^(-2)$

So the torque is $τ = 10.67 \cdot (9 π) N m = 301.6 N m$ $tau=10.67*(9pi) Nm=301.6Nm$

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

$I = \frac{1}{3} \cdot m L^{2}$ $I=1/3*mL^2$

$= \frac{1}{3} \cdot 8 \cdot 4^{2} = 42.67 k g m^{2}$ $=1/3*8*4^2=42.67kgm^2$

So,

The torque is $τ = 42.67 \cdot (9 π) = \frac{504}{5} π = 1206.4 N m$ $tau=42.67*(9pi)=504/5pi=1206.4Nm$

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What torque would have to be applied to a rod with a length of $4 m$ $4 m$ and a mass of $8 k g$ $8 kg$ to change its horizontal spin by a frequency $9 H z$ $9 Hz$ over $2 s$ $2 s$ ?

1 Answer

Explanation:

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What torque would have to be applied to a rod with a length of 4m4 m and a mass of 8kg8 kg to change its horizontal spin by a frequency 9Hz9 Hz over 2s2 s?

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What torque would have to be applied to a rod with a length of $4 m$ $4 m$ and a mass of $8 k g$ $8 kg$ to change its horizontal spin by a frequency $9 H z$ $9 Hz$ over $2 s$ $2 s$ ?