What torque would have to be applied to a rod with a length of $4 m$ $4 m$ and a mass of $2 k g$ $2 kg$ to change its horizontal spin by a frequency of $4 H z$ $4 Hz$ over $3 s$ $3 s$ ?

Question

What torque would have to be applied to a rod with a length of $4 m$ $4 m$ and a mass of $2 k g$ $2 kg$ to change its horizontal spin by a frequency of $4 H z$ $4 Hz$ over $3 s$ $3 s$ ?

1 Answer

Impact of this question

1385 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-03T11:27:44

The torque for the rod rotating about the center is $= 22.34 N m$ $=22.34Nm$
The torque for the rod rotating about one end is $= 89.36 N m$ $=89.36Nm$

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

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

$= \frac{1}{12} \cdot 2 \cdot 4^{2} = \frac{8}{3} k g m^{2}$ $=1/12*2*4^2= 8/3 kgm^2$

The rate of change of angular velocity is

$\frac{d ω}{d t} = \frac{4}{3} \cdot 2 π$ $(domega)/dt=(4)/3*2pi$

$= (\frac{8}{3} π) r a d s^{- 2}$ $=(8/3pi) rads^(-2)$

So the torque is $τ = \frac{8}{3} \cdot (\frac{8}{3} π) N m = \frac{64}{9} π N m = 22.34 N m$ $tau=8/3*(8/3pi) Nm=64/9piNm=22.34Nm$

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

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

$= \frac{1}{3} \cdot 2 \cdot 4^{2} = \frac{32}{3} k g m^{2}$ $=1/3*2*4^2=32/3kgm^2$

So,

The torque is $τ = \frac{32}{3} \cdot (\frac{8}{3} π) = \frac{256}{9} π = 89.36 N m$ $tau=32/3*(8/3pi)=256/9pi=89.36Nm$

Science

Math

Humanities

... and beyond

What torque would have to be applied to a rod with a length of $4 m$ $4 m$ and a mass of $2 k g$ $2 kg$ to change its horizontal spin by a frequency of $4 H z$ $4 Hz$ over $3 s$ $3 s$ ?

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 4m4 m and a mass of 2kg2 kg to change its horizontal spin by a frequency of 4Hz4 Hz over 3s3 s?

1 Answer

Explanation:

Related questions

Impact of this question

What torque would have to be applied to a rod with a length of $4 m$ $4 m$ and a mass of $2 k g$ $2 kg$ to change its horizontal spin by a frequency of $4 H z$ $4 Hz$ over $3 s$ $3 s$ ?