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

The radius of the gear is, 0.286624204 m

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*50 \pi`
`=100\pi` radian

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

and velocity(v) = 90 meter per minute

Use formula: Velocity(v)= radius(r)
`*` angular velocity
`(\omega)`

then, we write above formula as :
`r=(v)/(\omega)`

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

`r=(90)/(100\cdot3.14)`

`r=(90)/(314) =0.286624204 m` [as radian is unit less]