Question

One pulley rotates at 560 rpm. A second pulley, connected to the first by a belt, has a diameter of 12 in and rotates at 330 rpm. Find the diameter of the first pulley.

Answer 1

Let , d₁ = diameter of driver (first pulley)

n₁ = speed of driver

d₂ = diameter of follower (second pulley)

n₂ = speed of follower

length of the belt passes over the driver in one unit time = $\pi$d₁n₁

length of the belt passes over the driver in one unit time = $\pi$d₂n₂

since length of the belt is constant , therefore , $\pi$d₁n₁ = $\pi$d₂n₂

_{​​​​​​}   n₂/n_{1 =}  d₁/d₂

   330/560 = d₁/12

d₁ = (330*12)/560

d₁ = 7.1 in

Hence diameter of first pulley is found to be 7.1 in