What torque would have to be applied to a rod with a length of $1 m$ $1 m$ and a mass of $7 k g$ $7 kg$ to change its horizontal spin by a frequency $5 H z$ $5 Hz$ over $4 s$ $4 s$ ?

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What torque would have to be applied to a rod with a length of $1 m$ $1 m$ and a mass of $7 k g$ $7 kg$ to change its horizontal spin by a frequency $5 H z$ $5 Hz$ over $4 s$ $4 s$ ?

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Answer 1 · 2017-03-31T10:21:44

The torque, for the rod rotating about the center, is $= 4.58 N m$ $=4.58Nm$
The torque, for the rod rotating about one end, is $= 18.33 N m$ $=18.33Nm$

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

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

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

The rate of change of angular velocity is

$\frac{d ω}{d t} = \frac{5}{4} \cdot 2 π$ $(domega)/dt=(5)/4*2pi$

$= (\frac{5}{2} π) r a d s^{- 2}$ $=(5/2pi) rads^(-2)$

So the torque is $τ = \frac{7}{12} \cdot (\frac{5}{2} π) N m = \frac{35}{24} π = 4.58 N m$ $tau=7/12*(5/2pi) Nm=35/24pi=4.58Nm$

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

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

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

So,

The torque is $τ = \frac{7}{3} \cdot (\frac{5}{2} π) = \frac{35}{6} π = 18.33 N m$ $tau=7/3*(5/2pi)=35/6pi=18.33Nm$

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What torque would have to be applied to a rod with a length of $1 m$ $1 m$ and a mass of $7 k g$ $7 kg$ to change its horizontal spin by a frequency $5 H z$ $5 Hz$ over $4 s$ $4 s$ ?

1 Answer

Explanation:

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Science

Math

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What torque would have to be applied to a rod with a length of 1m1 m and a mass of 7kg7 kg to change its horizontal spin by a frequency 5Hz5 Hz over 4s4 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 $1 m$ $1 m$ and a mass of $7 k g$ $7 kg$ to change its horizontal spin by a frequency $5 H z$ $5 Hz$ over $4 s$ $4 s$ ?