What torque would have to be applied to a rod with a length of $7 m$ $7 m$ and a mass of $12 k g$ $12 kg$ to change its horizontal spin by a frequency $15 H z$ $15 Hz$ over $9 s$ $9 s$ ?

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What torque would have to be applied to a rod with a length of $7 m$ $7 m$ and a mass of $12 k g$ $12 kg$ to change its horizontal spin by a frequency $15 H z$ $15 Hz$ over $9 s$ $9 s$ ?

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Answer 1 · 2017-12-26T12:18:56

The torque for the rod rotating about the center is $= 513.1 N m$ $=513.1Nm$
The torque for the rod rotating about one end is $= 2052.5 N m$ $=2052.5Nm$

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 $m = 12 k g$ $m=12kg$

The length of the rod is $L = 7 m$ $L=7m$

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

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

$= \frac{1}{12} \cdot 12 \cdot 7^{2} = 49 k g m^{2}$ $=1/12*12*7^2= 49 kgm^2$

The rate of change of angular velocity is

$\frac{d ω}{d t} = \frac{15}{9} \cdot 2 π$ $(domega)/dt=(15)/9*2pi$

$= (\frac{10}{3} π) r a d s^{- 2}$ $=(10/3pi) rads^(-2)$

So the torque is $τ = 49 \cdot (\frac{10}{3} π) N m = 513.1 N m$ $tau=49*(10/3pi) Nm=513.1Nm$

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

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

$= \frac{1}{3} \cdot 12 \cdot 7^{2} = 196 k g m^{2}$ $=1/3*12*7^2=196kgm^2$

So,

The torque is $τ = 196 \cdot (\frac{10}{3} π) = 2052.5 N m$ $tau=196*(10/3pi)=2052.5Nm$

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What torque would have to be applied to a rod with a length of $7 m$ $7 m$ and a mass of $12 k g$ $12 kg$ to change its horizontal spin by a frequency $15 H z$ $15 Hz$ over $9 s$ $9 s$ ?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

What torque would have to be applied to a rod with a length of 7m7 m and a mass of 12kg12 kg to change its horizontal spin by a frequency 15Hz15 Hz over 9s9 s?

1 Answer

Explanation:

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Impact of this question

What torque would have to be applied to a rod with a length of $7 m$ $7 m$ and a mass of $12 k g$ $12 kg$ to change its horizontal spin by a frequency $15 H z$ $15 Hz$ over $9 s$ $9 s$ ?