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

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Answer 1 · 2018-06-09T14:17:52

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

We know that the wheel rotates at:

$ω = 2100 \frac{rev}{min}$ $omega=2100"rev"/"min"$

this corresponds to (in radiand per second):

$ω = \frac{2100 \cdot 2 π}{60} = 219.9 \approx 220 \frac{r a d}{s}$ $omega=(2100*2pi)/60=219.9~~220(rad)/s$

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

$v = ω r = 220 \cdot 0.1 = 22 \frac{m}{s}$ $v=omegar=220*0.1=22m/s$

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

Answer 2 · 2018-06-09T14:23:48

$22 m/s$ $"22 m/s"$

Frequency of wheel is

$f = 2100 rev/min$ $f = "2100 rev/min"$

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

$color(white)(f) = "35 Hz"$

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 ( $"v"$ ) of wheel is

$"v = R ω"$

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

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