Answer:
The radius of the gear is, 0.286624204 m
Step-by-step explanation:
A gear is driven by a chain that travels 90 m/min. If it makes 50 revolutions per minute. then find the radius of the gear
let angular velocity be [tex]\omega[/tex] , velocity be v and radius be r.
Given:
Angular velocity [tex](\omega)[/tex]=50 revolutions per minute
1 revolution = [tex]2\pi[/tex] radian
50 revolution= [tex]2\times50 \pi[/tex][tex]=100\pi[/tex] radian
therefore, [tex]\omega=100\pi[/tex] radian per minute
and velocity(v) = 90 meter per minute
Use formula: Velocity(v)= radius(r) [tex]\times[/tex] angular velocity [tex](\omega)[/tex]
then, we write above formula as : [tex]r=\frac{v}{\omega}[/tex]
Substitute the value of v and [tex]\omega[/tex] to solve for r: the constant value of pi i.e, [tex](\pi=3.14)[/tex]
[tex]r=\frac{90}{100\cdot3.14}[/tex]
[tex]r=\frac{90}{314} =0.286624204 m[/tex] [as radian is unit less]
