What would be the rotational speed of a driven sheave if its pitch diameter is 200 mm and the driver sheave with a 100 mm pitch diameter is rotating at 1800 RPM?

To determine the rotational speed of the driven sheave, the relationship between the pitch diameters of the sheaves and their rotational speeds must be applied. This relationship is described by the formula:

[ N_1 \times D_1 = N_2 \times D_2 ]

where ( N_1 ) and ( D_1 ) are the rotational speed and pitch diameter of the driver sheave, and ( N_2 ) and ( D_2 ) are the rotational speed and pitch diameter of the driven sheave.

In this scenario:

• The pitch diameter of the driver sheave ( D_1 ) is 100 mm.

• The rotational speed of the driver sheave ( N_1 ) is 1800 RPM.

• The pitch diameter of the driven sheave ( D_2 ) is 200 mm.

Rearranging the formula to find ( N_2 ), we get:

[ N_2 = \frac{N_1 \times D_1}{D_2} ]

Substituting in the known values:

[ N_2 = \frac{1800 , \text{RPM} \times 100 , \text{