two pulleys one with radius 2 inches and the other with radi

two pulleys, one with radius 2 inches and the other with radius 8 inches are connected by a belt. if the 2 inch pulley is caused to rotate at 3 revolutions per minute, determine the revolutions per minute by the 8 inch pulley.

Please explain each step, thanks!

Solution

Each time the pulley goes around, the belt advances by the circumference of the pulley.

Linear speed of the belt = circumference * revolutions per minute

=2r * rpms

For 2 inch pulley = 2* 2 inch *3rpm since r=2 inch

For 8 inch pulley =2* 8inch *xrpm since r=8 inch and let x is revolutions per minute for 8 inch pulley

2 * 2 inch *3rpm = 2 * 8inch *xrpm   since the linear speed is the same for both pulleys

x rpm =6/8 =3/4 since cancelling 2 both side of the equation

Therefore

For The 8 inch pulley the revolutions per minute is 3/4 revolutions per minute