In the pulley system below, how fast does pulley D rotate, if pulley A rotates at 100 rpm?

In the pulley system below, how fast does pulley D rotate, if pulley A rotates at 100 rpm?

Detailed Explanation

A larger pulley causes a smaller pulley to rotate faster by the ratio of their diameters. If pulley A rotates at 100 rpm, then pulley B rotates at \(\frac{\mathrm{100 \times 4} }{\mathrm{10} } = 40\) rpm.

Since C is directly connected to B it rotates at the same rate (40 rpm).

Finally, pulley D will rotate at \(40 \times \frac{\mathrm{5} }{\mathrm{16} } = 12.5\) rpm.

Since C is directly connected to B it rotates at the same rate (40 rpm).

Finally, pulley D will rotate at \(40 \times \frac{\mathrm{5} }{\mathrm{16} } = 12.5\) rpm.