# TrigonometryLinear speed of a flywheel

#### karush

##### Well-known member
A flywheel with a $15cm$ diameter is rotating at a rate of $\displaystyle\frac{7 rad}{s}$
What is the linear speed of a point on the rim, in $\displaystyle\frac{cm}{min}$.

$s=r\theta$ so $7.5(7) = 152$cm
then $\displaystyle v=\frac{s}{t}=\frac{152cm}{s}\cdot\frac{60s}{min}=\frac{1320cm}{min}$

I am not sure just what a Radian (rad) is in this, so hope I didn't make this to simple. don't have answer so hope mine ok

#### MarkFL

Staff member
Your method is correct (but you have made some arithmetical errors)...I would write:

$$\displaystyle v=r\omega=\frac{15}{2}\text{ cm}\cdot7\frac{1}{\text{s}}\cdot\frac{60\text{ s}}{1\text{ min}}=?$$

#### karush

##### Well-known member
Your method is correct (but you have made some arithmetical errors)...I would write:

$$\displaystyle v=r\omega=\frac{15}{2}\text{ cm}\cdot7\frac{1}{\text{s}}\cdot\frac{60\text{ s}}{1\text{ min}}=?$$

$\displaystyle\frac{3150 cm}{min}$

#### MarkFL

Staff member
$\displaystyle\frac{3150 cm}{min}$
Correct. The method you used is:

$$\displaystyle v=\frac{s}{t}=\frac{r\theta}{t}=r\frac{\theta}{t}$$

Now defining the angular velocity $\omega$ to be:

$$\displaystyle \omega=\frac{\theta}{t}$$

we then have:

$$\displaystyle v=r\omega$$

That is, the linear velocity $v$ is the product of the radius of motion and the angular velocity.

Did you find the error in your previous calculations?

#### karush

##### Well-known member
let me see if this set up ok

a wheel with $30cm$ radius is rotating at a rate of $\displaystyle{3rad}{s}$ what is v in $\displaystyle\frac{m}{s}$

 $\displaystyle v=r\omega$ $\displaystyle 30\text{ cm}\cdot3\frac{1}{\text{s}}\cdot \frac{m}{100\text{cm}}=$

#### MarkFL

Staff member
let me see if this set up ok

a wheel with $30cm$ radius is rotating at a rate of $\displaystyle{3rad}{s}$ what is v in $\displaystyle\frac{m}{s}$

 $\displaystyle v=r\omega$ $\displaystyle 30\text{ cm}\cdot3\frac{1}{\text{s}}\cdot \frac{m}{100\text{cm}}=$
Yes, that is correct.

#### karush

##### Well-known member
oops just noticed the ans should be in $$\displaystyle \frac{\text {m}}{\text {min}}$$

so...

 $\displaystyle 30\text{ cm}\cdot \frac{3}{\text{s}} \cdot \frac{60 \text { s}}{\text { min}} \cdot \frac{\text { m}}{100\text{ cm}}=\frac{54 \text {m}}{\text {min}}$

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Did you find the error in your previous calculations?
yes I had 152 cm it should be 52.5 cm