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

2 Answers
Jun 9, 2018

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.

Jun 9, 2018

#"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"#