How to find frequency of rotational motion without knowing radius?

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How to find frequency of rotational motion without knowing radius?

$v_{1}$ $v_1$ =3m/s, $v_{2}$ $v_2$ =2m/s, $r_{2}$ $r_2$ =r-10cm

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Answer 1 · 2017-04-02T13:18:50

$ω = 10 \frac{r a d i a n s}{s}$ $omega = 10 (radians)/s$

Explanation:

I assume that we are referring to a rigid object that rotates at a constant angular frequency $ω$ $omega$ around some axis of rotation.

We know the linear speeds $v_{1} = 3 \frac{m}{s}$ $v_1=3 m/s$ and $v_{2} = 2 \frac{m}{s}$ $v_2=2 m/s$ at two points $1$ $1$ and $2$ $2$ on the rotating solid, and we know that the radii (distance from the axis of rotation) $r_{1}$ $r_1$ and $r_{2}$ $r_2$ at these two points are related as $r_{2} = r_{1} - 10 c m$ $r_2 = r_1 - 10cm$ .

For rigid rotation, it holds for any point on the solid that
$ω = \frac{v}{r}$ $omega = v/r$ , where $v$ $v$ is the linear speed at that point and $r$ $r$ is the distance from the axis of rotation.

Therefore we know that
$ω = \frac{v_{1}}{r_{1}} = \frac{v_{2}}{r_{2}} = ω$ $omega = v_1/r_1 = v_2/r_2 = omega$ ,
which gives that
$\frac{v_{1}}{r_{1}} = \frac{v_{2}}{r_{1} - 10 c m}$ $v_1/r_1 = v_2/(r_1 - 10 cm)$ .

Now we can solve for $r_{1}$ $r_1$ by multiplying both sides by the denominators
$v_{1} (r_{1} - 10 c m) = v_{2} r_{1}$ $v_1(r_1 - 10 cm)= v_2r_1$ ,
$r_{1} = 10 c m \frac{v_{1}}{v_{1} - v_{2}} = 30 c m$ $r_1 = 10 cm v_1/(v_1-v_2) = 30 cm$ .

Using our newfound knowledge of the radius $r_{1}$ $r_1$ , we get that
$ω = \frac{v_{1}}{r_{1}} = \frac{3 \frac{m}{s}}{30 c m} r a d i a n s = \frac{3 \frac{m}{s}}{0.3 m} r a d i a n s = 10 (\frac{r a d i a n s}{s})$ $omega = v_1/r_1 = (3 m/s)/(30 cm) radians= (3 m/s)/(0.3 m) radians = 10 ((radians)/s)$ .

Check that you get the same answer when using $v_{2}$ $v_2$ and $r_{2}$ $r_2$ .

Answer 2 · 2017-04-02T13:25:33

Depends what you're asking.

Explanation:

It looks like there is a typo in your question. If what you are really saying is this: $r_{2} = r_{1} - 10 c m$ $r_2= r_color(red)(1) -10cm$ then:

$ω = \frac{3}{r_{1}} = \frac{2}{r_{1} - 10} \Rightarrow r_{1} = 30 cm \Rightarrow ω = 10 rad/s$ $omega = 3/r_1 = 2/(r_1 - 10) implies r_1 = 30 " cm" implies omega = 10 "rad/s"$

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How to find frequency of rotational motion without knowing radius?

$v_{1}$ $v_1$ =3m/s, $v_{2}$ $v_2$ =2m/s, $r_{2}$ $r_2$ =r-10cm

2 Answers

Explanation:

Explanation:

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Science

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How to find frequency of rotational motion without knowing radius?

v_1v1v_1 =3m/s, v_2v2v_2 =2m/s, r_2r2r_2 =r-10cm

2 Answers

Explanation:

Explanation:

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$v_{1}$ $v_1$ =3m/s, $v_{2}$ $v_2$ =2m/s, $r_{2}$ $r_2$ =r-10cm