A wheel with 6 cogs meshes with a larger wheel with 14 cogs. When the smaller wheel makes 21 revolutions, how many revolutions does the larger wheel make?

Given data

• Small wheel: 6 cogs
• Large wheel: 14 cogs
• Small wheel revolutions = 21

Concept / Approach

• Teeth engagements are equal at the mesh. Total teeth passed by small wheel = total teeth passed on large wheel's rim.
• Revolutions are inversely proportional to the number of cogs.

Step-by-step calculation

Teeth passed by small wheel = 21 × 6 = 126 teethRevolutions of large wheel = 126 ÷ 14 = 9

Verification

Inverse ratio check: rev_L / rev_S = 6/14 ⇒ rev_L = 21 × 6/14 = 9.

Common pitfalls

• Using direct ratio 14/6 instead of inverse.

Final Answer

9