Problem

A bicycle has wheels 700 mm in diameter and a gear set with the dimensions given in the ta...

A bicycle has wheels 700 mm in diameter and a gear set with the dimensions given in the table below.

Figure P6.30

Crank
Sprocket	C1	C2	C3
No. of Cogs	26	36	48
Radius (mm)	52.6	72.8	97.0

Cassette (9 speeds)
Sprocket	S1	S2	S3	S4	S5	S6	S7	S8	S9
No. of Cogs	11	12	14	16	18	21	24	28	34
Radius (mm)	22.2	24.3	28.3	32.3	36.4	42.4	48.5	56.6	68.7

If a cyclist has a cadence of 68 rpm, determine which combination of chain ring (a sprocket mounted on the crank) and (rear) sprocket would most closely make the rear wheel rotate with an angular speed of 127 rpm. Having found a chain ring/sprocket combination, determine the wheel’s exact angular speed corresponding to the chosen chain ring/sprocket combination and the given cadence.

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