Activity 1.6 Gear Ratios

A student claims: “If the driving gear is smaller than the driven gear, the output speed will increase.” Using the idea of gear ratio and the note that the left gear is driving and the right gear is driven, evaluate the claim.

• The claim is correct because a smaller driving gear always turns a larger driven gear faster.

• The claim is incorrect; a smaller driving gear driving a larger driven gear decreases output speed.

• The claim cannot be evaluated without knowing torque.

• The claim is correct only when both gears have the same number of teeth.

When calculating gear ratio using number of teeth, which gear’s teeth go in the numerator to match the same ratio value?

• Teeth of driving gear

• Teeth of driven gear

• Average teeth of both gears

• Teeth of the idler gear

A student calculates gear ratio as rotations of driven gear over rotations of driving gear. To keep the same numerical value using teeth, which expression should they use?

• Teeth of driven gear over teeth of driving gear

• Teeth of driving gear over teeth of driven gear

• Teeth of driving gear plus teeth of driven gear

• Teeth of driven gear minus teeth of driving gear

You need to increase torque at the output while accepting a reduction in speed. Which tooth-count choice best meets this goal for a single gear pair?

• Driving gear has fewer teeth than the driven gear.

• Driving gear and driven gear have the same teeth.

• Driving gear has more teeth than the driven gear.

• Teeth count does not affect torque.

Consider a two-gear system intended to keep output speed equal to input speed. Which pair achieves this using teeth counts?

• 36T driving to 12T driven

• 30T driving to 30T driven

• 24T driving to 72T driven

• 15T driving to 45T driven

In a gear train, the driving gear has 16 teeth and the driven gear has 64 teeth. Using teeth-count ratios, what happens to speed and torque at the driven gear?

• Speed increases 4×; torque decreases 4×.

• Speed decreases 4×; torque increases 4×.

• Speed stays the same; torque stays the same.

• Speed increases 2×; torque increases 2×.

Use proportional reasoning with teeth counts to decide which gear in the train A (36T) → B (48T) → C (12T) will have the greatest angular speed.

• Gear A

• Gear B

• Gear C

• All have equal speed

You must choose a driven gear to match the input speed as closely as possible. Which choice best meets that goal based on the examples?

• Match the driven gear’s teeth count to the driving gear’s teeth count

• Use the smallest possible driven gear

• Use the largest possible driven gear

• Insert multiple idlers until the speeds match

Looking at the picture, what is the gear ratio?

• 6:10
• 3:10
• 10:6
• 3:5

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

True or false; the starting gear is the input gear.

• true
• false
• not enough information