In the illustration, If gear A has 72 teeth,...

Question 1 of 270705eccefa3bacbc34ba4d47ce1

In the illustration, If gear A has 72 teeth, gear B has 64 teeth, gear C has 24 teeth and gear D has 36 teeth, what is the RPM of the gear D if gear A is turning at 100 RPM? See illustration MO-0088.

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Question 1 of 27070

In the illustration, If gear A has 72 teeth, gear B has 64 teeth, gear C has 24 teeth and gear D has 36 teeth, what is the RPM of the gear D if gear A is turning at 100 RPM? See illustration MO-0088.

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🔍 Key Concepts

• Relationship between gear speed (RPM) and number of teeth: the meshing gears satisfy $N_1 T_1 = N_2 T_2$ so speed is inversely proportional to teeth. • Understanding a compound gear train: gears B and C are on the same shaft in the illustration, so they turn at the same RPM even though they have different teeth counts. • Overall speed ratio is the product of each stage (A to B, then C to D).

💭 Think About

• First, use the tooth counts of gears A and B to find the RPM of gear B when gear A turns at 100 RPM. What formula connects speed and number of teeth for two meshing gears? • Since gears B and C are on the same shaft, what can you say about their RPMs? How does that help you set up the next calculation from gear C to gear D? • After you find the RPM of gear D from gear C, compare it to the original RPM of gear A. Is the final gear expected to be faster or slower overall, based on the tooth ratios at each stage?

✅ Before You Answer

• Be sure you are using the inverse ratio of teeth to get RPM (more teeth → lower RPM, fewer teeth → higher RPM). • Confirm you treat B and C as a compound gear with the same RPM, not as separate free-spinning gears. • Multiply the two stage ratios sequentially (A→B and C→D) and then compare your numerical result carefully with the nearest multiple‑choice value.