# A grinding wheel has a diameter of 200mm. If it rotates at 2100 rev/min. What is the circumferential speed?

Jun 9, 2018

I got $22 \frac{m}{s}$

#### Explanation:

We know that the wheel rotates at:

$\omega = 2100 \text{rev"/"min}$

this corresponds to (in radiand per second):

$\omega = \frac{2100 \cdot 2 \pi}{60} = 219.9 \approx 220 \frac{r a d}{s}$

now, the linear speed $v$ (which I think is your circumferencial speed) is:

$v = \omega r = 220 \cdot 0.1 = 22 \frac{m}{s}$

where I changed the diameter into meters and divided by $2$ to get the radius.

Jun 9, 2018

$\text{22 m/s}$

#### Explanation:

Frequency of wheel is

$f = \text{2100 rev/min}$

color(white)(f) = 2100 "rev"/cancel"min" × (1 cancel"min")/("60 s")

$\textcolor{w h i t e}{f} = \text{35 Hz}$

Angular frequency of wheel is

ω = 2 π f

color(white)(ω) = 2 × 22/7 × "35 Hz"

color(white)(ω) = "220 rad/s"

Circumferential speed ($\text{v}$) of wheel is

$\text{v = R ω}$

color(white)("v") = 200/2 × 10^-3\ "m × 220 rad/s"

color(white)("v") = 22\ "m/s"