Linear speed and Angular speed
Linear speed: the distance traveled divided by time.
An object move from A to B, the distance is `d = θtimes r`
than the linear speed
` v = d/t = (θr)/t`
Angular speed: the angle swept divided by time.
`ω = (θ)/t`
therefor ,we can get
`v =ω times r `
Example:
Suppose you are sitting on a ferris wheel that has a radius of 10 meter. It takes 4 minutes for the wheel to rotate 3.5 revolutions.
What is the angular and linear speed of the wheel?
Solution:
`1` revolution = `2π \ rad`
`3.5` revolution = `3.5 times 2π \ rad = 7π\ rad`
`ω = (7π)/4 = 5.5\ rad//mi n`
`v = ωr = 5.5 times 10 = 55\ m//mi n`