Question

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

Answer 1

I got `22m/s`

Explanation:

We know that the wheel rotates at:

`omega=2100"rev"/"min"`

this corresponds to (in radiand per second):

`omega=(2100*2pi)/60=219.9~~220(rad)/s`

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

`v=omegar=220*0.1=22m/s`

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

Answer 2

`"22 m/s"`

Explanation:

Frequency of wheel is

`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"`