Can You Guys Explain This?

Question

To lift heavy objects with a motor people sometimes use a system that reduces angular speed but increases torque, like the one shown below. The motor spins a small rotor, r1, which is connected by a belt to a larger rotor, r2. This large rotor is attached to, and rotates concentrically with, another small rotor, r3, that is attached to the rope that lifts the object. The radius of the rotor attached to the motor (r1) is 10 cm, the radius of the large rotor (r2) is 40 cm and the radius of the small concentric rotor (r3) is 8cm. At what angular speed (in rpm) does the motor rotate to lift the box at a constant speed of 120π cm/min?

Answer 1

The circumference of r₃ is 16π .cm

To lift at 120π cm/min, it must rotate (120π / 16π) / min or 7.5 rpm

The circumference of r₂ is 80π cm. It is also rotating at 7.5 rpm.↑

r₂ is pulling the belt at 600π cm / min.

The circumference of r₁ is 20π cm.

(600π cm/min) / 20π cm = 30 rpm.