What torque would have to be applied to a rod with a length of $12 m$ $12 m$ and a mass of $7 k g$ $7 kg$ to change its horizontal spin by a frequency $4 H z$ $4 Hz$ over $8 s$ $8 s$ ?

Question

What torque would have to be applied to a rod with a length of $12 m$ $12 m$ and a mass of $7 k g$ $7 kg$ to change its horizontal spin by a frequency $4 H z$ $4 Hz$ over $8 s$ $8 s$ ?

1 Answer

Impact of this question

1251 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-16T09:04:02

The torque for the rod rotating about the center is $= 263.9 N m$ $=263.9Nm$
The torque for the rod rotating about one end is $= 1055.6 N m$ $=1055.6Nm$

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

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

$= \frac{1}{12} \cdot 7 \cdot 12^{2} = 84 k g m^{2}$ $=1/12*7*12^2= 84 kgm^2$

The rate of change of angular velocity is

$\frac{d ω}{d t} = \frac{4}{8} \cdot 2 π$ $(domega)/dt=(4)/8*2pi$

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

So the torque is $τ = 84 \cdot (π) N m = 84 π N m = 263.9 N m$ $tau=84*(pi) Nm=84piNm=263.9Nm$

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

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

$= \frac{1}{3} \cdot 7 \cdot 12^{2} = 336 k g m^{2}$ $=1/3*7*12^2=336kgm^2$

So,

The torque is $τ = 336 \cdot (π) = 336 π = 1055.6 N m$ $tau=336*(pi)=336pi=1055.6Nm$

Science

Math

Humanities

... and beyond

What torque would have to be applied to a rod with a length of $12 m$ $12 m$ and a mass of $7 k g$ $7 kg$ to change its horizontal spin by a frequency $4 H z$ $4 Hz$ over $8 s$ $8 s$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What torque would have to be applied to a rod with a length of 12m12 m and a mass of 7kg7 kg to change its horizontal spin by a frequency 4Hz4 Hz over 8s8 s?

1 Answer

Explanation:

Related questions

Impact of this question

What torque would have to be applied to a rod with a length of $12 m$ $12 m$ and a mass of $7 k g$ $7 kg$ to change its horizontal spin by a frequency $4 H z$ $4 Hz$ over $8 s$ $8 s$ ?