Question

A car traveling at 50 mph goes around a curve that has a radius of 75 feet. What is the car's angular velocity in revolutions per minute to the nearest tenth?

Answer 1

`n= 9,3(rev)/(min)`

Explanation:

tangentian velocity (v)is bound to angular velocity (`omega`) by the relationship:
`v = omega xx r`
hence
`omega= v/r`
1 mile = 5280 ft
1 h = 3600 s
`1(rev)/(min)= (2 pi)/(60 s) = 0,104 (rad)/s`
`1 (rad)/s = 9,55(rev)/(min)`
`omega= 50 xx ((5280 ft)/(3600 s))/( 75 ft)= 0,978 (rad)/s`
`n= 0,978 xx 9,55(rev)/(min)= 9,34(rev)/(min)`