Trigonometry

Question

A belt connects two pulleys with radii 2.7 inches and 4.5 inches. The larger pulley is rotating at 20 rpm. 

A) What is the angular speed of the larger pulley, in radians per minutes? 

 

B) What is the linear speed of the belt, in inches per minute?

 

C) What is the angular speed of the smaller pulley, in radians per minutes?

Answer 1

smaller pulley has radii r₁ = 2.7 inches

larger pulley has radii  r₂  = 4.5 inches

frequency  f = 20 rpm

 

a)angular speed ω₂ = 2*pi*f = 2*pi*20=125.66 rad/min.

 

b)linear speed v = ω₂r₂  (as belt revolves over larger pulley)

                        = 125.66 * 4.5 

                        = 551.48 inches/min

 

c)angular speed of smaller pulley ω₁=v/r₁ = 551.48/2.7 =204.25 rad/min.