Question

a gear is driven by a chain that travels 90 m/min. Find the radius of the gear if it makes 50 revolutions per minute

Answer 1

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 $\omega$ , velocity be v and  radius be r.

Given:

Angular velocity $(\omega)$=50 revolutions per minute

1 revolution = $2\pi$ radian

50 revolution= $2\times50 \pi$$=100\pi$ radian

therefore, $\omega=100\pi$ radian per minute

and velocity(v) = 90 meter per minute

Use formula: Velocity(v)= radius(r) $\times$ angular velocity $(\omega)$

then, we write above formula as :  $r=\frac{v}{\omega}$

Substitute the value of v and $\omega$ to solve for r:  the constant value of pi i.e, $(\pi=3.14)$

$r=\frac{90}{100\cdot3.14}$

$r=\frac{90}{314} =0.286624204 m$     [as radian is unit less]