What torque would have to be applied to a rod with a length of $4 m$ $4 m$ and a mass of $3 k g$ $3 kg$ to change its horizontal spin by a frequency of $5 H z$ $5 Hz$ over $1 s$ $1 s$ ?

Question

What torque would have to be applied to a rod with a length of $4 m$ $4 m$ and a mass of $3 k g$ $3 kg$ to change its horizontal spin by a frequency of $5 H z$ $5 Hz$ over $1 s$ $1 s$ ?

1 Answer

Impact of this question

1697 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-16T17:50:09

$τ \approx 126 N m$ $tau≈126Nm$

Explanation:

The net torque, $τ$ $tau$ , can be expressed in terms of the moment of inertia and angular acceleration, where $τ = I α$ $tau=Ialpha$ .

Assuming that this is a thin, rigid rod, with the axis of rotation through its center, the moment of inertia, $I$ $I$ , of the rod is given by $\frac{1}{12} M L^{2}$ $1/12ML^2$ , where $M$ $M$ is the mass of the rod and $L$ $L$ is its length. If the rod is rotated about its end, $I = \frac{1}{3} M L^{2}$ $I=1/3ML^2$ . I will show the calculation for the axis of rotation through the center. We are given both $L$ $L$ and $M$ $M$ . Thus,

$I = \frac{1}{12} \cdot 3 k g \cdot {(4 m)}^{2}$ $I=1/12*3kg*(4m)^2$

$I = 4 k g m^{2}$ $I=4kgm^2$

The angular acceleration of the rod as it rotates, $α$ $alpha$ , can be calculated from the given values of time and frequency, where $alpha=(Δomega)/( Δt)$ . We can find $omega$ from the given frequency of $5Hz$ , as $omega=2pif$ .

$omega=2pi(5s^-1)$

$omega=10pi(rad)/s$

Because the problem states that the frequency changed by this amount, this is $Δomega$ . We are given that this took place over $1s$ , which is our $Δt$ value. Thus,

$alpha=(10pi(rad/s))/(1s)$

$alpha=10pi(rad)/s^2$

Now that we have all of the values we need, we can calculate the torque.

$tau=Ialpha$

$tau=4kgm^2*10pi(rad)/s^2$

$tau=40piNm$

$tau≈126Nm$

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 $3 k g$ $3 kg$ to change its horizontal spin by a frequency of $5 H z$ $5 Hz$ over $1 s$ $1 s$ ?

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 4 m4m4 m and a mass of 3 kg3kg3 kg to change its horizontal spin by a frequency of 5 Hz5Hz5 Hz over 1 s1s1 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 $3 k g$ $3 kg$ to change its horizontal spin by a frequency of $5 H z$ $5 Hz$ over $1 s$ $1 s$ ?