Question

a line shaft rotating at 300 rpm is connected to a grinding wheel by the pulley assembly shown. if the grinder shaft must turn at 1100 rpm, what size pulley should be attached to the line shaft? if the grinder shaft must turn at 1100 rpm, a in. pulley should be attached to the line shaft.

Explanation:

Step1: Set up the proportion

The relationship between pulley size (\(d\)) and rotational speed (\(n\)) is \(d_1n_1 = d_2n_2\). Let \(d_1=x\), \(n_1 = 300\) rpm, \(d_2 = 6\) in, \(n_2=1100\) rpm.

Step2: Solve for \(x\)

Substitute the values into the formula: \(x\times300=6\times1100\). Then \(x=\frac{6\times1100}{300}\).
Calculate \(\frac{6\times1100}{300}=\frac{6600}{300}=22\).

Answer:

\(22\)