Question

Find the diameter of a pulley which is driven at 360 rpm by a belt moving at 40 ft/s.

Then in 1 s the pulley turns through an angle theta measuring 12 pi radians and a point on the rim travels a distance s= 40 ft.

Answer 1

let the diameter be D ft
in one rotation the belt moves Dπ ft.

The wheel rotates at 360 rpm, or at 60 rotations per second
In that 1 second the belt covers 40 ft.
so 60(Dπ) = 40
Dπ = 2/3
D = 2/(3π) ft = appr .2122 ft or appr 2.546 inches

Answer 2

Circumference = pi*D = 3.14D ft.

Vp = Vb, Vp is velocity of the pulley, and Vb is velocity of the belt.

3.14D ft/rev * 360rev/60s = 40.
D = 2.12 Ft. = Diameter of the pulley.

Answer 3

360 rpm=6 rps

(360rev./min.)(1min./60sec.)=6rps