# Math Help - Linear and angular velocity 2 problems?

1. ## Linear and angular velocity 2 problems?

My first problem is change 85 radians per second to revolutions per minute I know you have to use dimensional analysis.
So would It be
85 rad I am not sure how to set up the rest
-------=
1 sec

My second problem is this find the linear velocity in millimeters per second for each hand which is 30 millimeters long
I know the formula is v=r(angular velocity)
I know r= 30 but I am unsure how to find angular velocity
Can anyone help me with these two problems?

2. Originally Posted by homeylova223
My first problem is change 85 radians per second to revolutions per minute I know you have to use dimensional analysis.
So would It be
85 rad I am not sure how to set up the rest
-------=
1 sec

My second problem is this find the linear velocity in millimeters per second for each hand which is 30 millimeters long
I know the formula is v=r(angular velocity)
I know r= 30 but I am unsure how to find angular velocity
Can anyone help me with these two problems?
$\displaystyle 85 \, \frac{rad}{sec} \cdot \frac{60 \, sec}{1 \, min} \cdot \frac{1 \, rev}{2\pi \, rad}$

second problem ... what do you mean by "each hand" ? hands of a clock?

3. Hello, homeylova223!

I'll baby-step through the procedure . . .

My first problem is change 85 radians per second to revolutions per minute.

You started correctly.

$\text{We have: }\:\dfrac{85\text{ rad}}{1\text{ sec}}\;\hdots\text{ and we want: }\:\dfrac{x\text{ rev}}{1\text{ min}}$

Our game plan: replace "rad" with "rev", and replace "sec" with "min".

We want to change radians to revolutions.

We know that: . $1\text{ rev} \:=\:2\pi\text{ rad}$

Form a fraction with the two equivalent quantities.
. . $\text{There are two possible fractions: }\:\dfrac{2\pi\text{ rad}}{1\text{ rev}} \,\text{ or }\,\dfrac{1\text{ rev}}{2\pi\text{ rad}}$

Choose the fraction that will cancel the "rads", and multiply.

. . $\displaystyle \frac{85\,\rlap{///}\text{rad}}{1\,\text{sec}} \times \frac{1\,\text{rev}}{2\pi\,\rlap{///}\text{rad}} \;=\;\frac{85\,\text{rev}}{2\pi\,\text{sec}}$

We want to change "sec" to "min".

We know that: . $60\text{ sec} \,=\,1\text{ min}.$

Form a fraction with the two equivalent quantities.
. . There are two possible fractions: . $\dfrac{60\text{ sec}}{1\text{ min}}\,\text{ or }\,\dfrac{1\text{ min}}{60\text{ sec}}$

Choose the fraction that will cancel the "secs", and multiply.

. . $\displaystyle \frac{85\,\text{rev}}{2\pi\,\rlap{///}\text{sec}} \times \frac{60\,\rlap{///}\text{sec}}{1\,\text{min}} \;=\; \frac{2550\text{ rev}}{\pi\text{ min}}$

Therefore: . $85\text{ rad/sec} \;\approx\;811.7\text{ rpm.}$

4. Yeah it is second hand on a clock I think.

5. Originally Posted by homeylova223
Yeah it is second hand on a clock I think.
a second hand completes 1 revolution in 1 minute ... convert that to radians per second.

$v = r\omega$

6. I have a quick question when I multiplied 85 rev x 60 I get 5100 do you divide by half?

7. Originally Posted by homeylova223
I have a quick question when I multiplied 85 rev x 60 I get 5100 do you divide by half?
no, divide by $2\pi$ ...

$\displaystyle \frac{85 \cdot 60}{2\pi}$