Question

Two pulleys one with radius 7 inches and the other one with radius 23 inches are connected by a belt. If the 7-inch pulley is rotating at 12 revolutions per minute, determine the revolutions per minute of the 23-inch pulley.

Answer 1

The belt must be going at the same tangential velocity when in contact with the pulleys, if not slipping. The tangential velocity is just the circumference of the pulley, 2 pi R, multiplied by the number of revolutions per minute.

2 pi (7) (12/min) = 2 pi (23) (x/min)

Find x.

Answer 2

84pi/23

Answer 3

v = ωr

12(2pi) (7) = ω (23)

w = 168pi/23 rad/min

Answer 4

i see, ty

Answer 5

1 rev/min = 2 pi rad/min