Question

A wheel with a 15cm diameter is rotating at a rate of 7 radians/sec. what is the linear speed of a point on its rim, in meters per minute?

cant seem to figure this one out, any advice?

Answer 1

The key here is relate linear and angular velocity,

`nu = romega`

Given,

`r = d/2 = 7.5"cm" = 0.075"m"`

`omega = (7"rad")/"s"`

Hence,

`nu = romega = (0.525"m")/"s" * (60"s")/"min" = (31.5"m")/"min"`

is the speed of a point about the circumference of wheel.

Answer 2

`31.5 m/min`

Explanation:

Understanding a few things, that you probably know, can lead you to the answer without remembering the formula. One revolution is a rotation of `2*pi radians`. In the time of one revolution, the point on the rim will travel a distance equal to the perimeter: `pi*d`.

The perimeter is `pi*d = pi*0.15 m = 0.471 m`

One full revolution, or `2*pi radians = 6.28 radians`, so 7 radians is slightly more than one full revolution. How much more? By a ratio of

`7/(2*pi) = 1.114`

So the distance, s, it goes in 1 second at `7 "radians"/s` will be

`s = 1.114*"the perimeter" = 1.114*471 m = 0.525 m`

So in 1 second, that point on the rim went 0.525 m -- that means the linear speed is `0.525 m/s`. They want the answer in meters per minute, so

`0.525 m/s * ((60 s)/(1 min)) = 31.5 m/min`

I hope this helps,
Steve