Gears and Gear Ratios Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

A hand-cranked emergency siren uses a compound gear train to amplify the rotational speed of the crank. The crank is directly attached to Gear A, which has $50$ teeth. Gear A meshes with Gear B, which has $10$ teeth. Gear B shares a solid shaft with Gear C, which has $40$ teeth. Finally, Gear C meshes with Gear D, which has $10$ teeth and is directly attached to the siren's rotor. If the operator turns the crank at a constant speed of $30\text{ rpm}$ , what is the rotational speed of the siren's rotor?

Show answer & explanation

Answer: 600

Answer

600 rpm

The system consists of two gear pairs that both increase speed. The first pair (

50

teeth driving

10

teeth) increases the speed by a factor of

5

. The second pair (

40

teeth driving

10

teeth) increases the speed by a factor of

4

. The total speed multiplier is

5 \times 4 = 20

. Multiplying the input speed of

30\text{ rpm}

by

20

yields the final output speed of

600\text{ rpm}

.

Step-by-Step Solution

1

Determine the speed multiplier for the first gear pair.

Ratio =

50 / 10 = 5

Gear A drives Gear B. A larger gear driving a smaller gear increases rotational speed proportionally to their tooth count.

2

Determine the speed multiplier for the second gear pair.

Ratio =

40 / 10 = 4

Gear C drives Gear D. Both pairs are independent in tooth count, but Gear C rotates at the same speed as Gear B because they share a shaft.

3

Calculate the total mechanical advantage for speed.

Total multiplier =

5 \times 4 = 20

In a compound gear train, the total speed ratio is the product of the individual gear pair ratios.

4

Calculate the final output speed.

30 \times 20 = 600\text{ rpm}

Multiply the input speed by the total speed multiplier to find the output speed.

Key Concept

Compound Gear Trains and Speed Ratios

Question 2Question →

A mechanical winch uses a compound gear train to lift heavy loads. The input motor drives Gear A (30 teeth) clockwise at $300$ RPM. Gear A meshes directly with Gear B (45 teeth). Gear C (15 teeth) is fixed to the same shaft as Gear B, meaning they rotate together. Gear C meshes with an idler Gear D (30 teeth), which in turn meshes with the output Gear E (60 teeth).

Based on this configuration, what is the rotational speed and direction of the output Gear E?

50 RPM, counter-clockwise

50 RPM, clockwise

150 RPM, clockwise

1800 RPM, counter-clockwise

Show answer & explanation

Answer: 50 RPM, counter-clockwise

Answer

The correct answer is 50 RPM, counter-clockwise.

The correct answer is calculated by tracking the speed reduction and direction reversal across each mesh. Shaft 2 rotates at 200 RPM CCW (

300 \times \frac{30}{45}

). Shaft 3 (idler) rotates at 100 RPM CW (

200 \times \frac{15}{30}

). The final output shaft rotates at 50 RPM CCW (

100 \times \frac{30}{60}

).

Step-by-Step Solution

1

Calculate the speed and direction of the second shaft (Gears B and C).

Gear B speed =

300 \times \frac{30}{45} = 200

RPM. Direction = counter-clockwise.

When meshing, speed is inversely proportional to tooth count. Meshing gears rotate in opposite directions. Because Gears B and C share a shaft, Gear C also rotates at 200 RPM counter-clockwise.

2

Calculate the speed and direction of the idler Gear D.

Gear D speed =

200 \times \frac{15}{30} = 100

RPM. Direction = clockwise.

Gear C drives Gear D. The ratio is

\frac{15}{30}

, and the direction reverses from counter-clockwise to clockwise.

3

Calculate the final speed and direction of output Gear E.

Gear E speed =

100 \times \frac{30}{60} = 50

RPM. Direction = counter-clockwise.

Gear D drives Gear E. The ratio is

\frac{30}{60}

, and the direction reverses from clockwise to counter-clockwise.

Key Concept

Compound Gear Trains and Idler Mechanics

Question 3Question →

A vintage printing press utilizes a compound gear train to feed paper. Shaft 1 is the input and is driven at $120$ RPM in a counter-clockwise direction. Gear A ( $40$ teeth) is mounted on Shaft 1 and meshes directly with Gear B ( $20$ teeth), which is mounted on Shaft 2. Also rigidly mounted on Shaft 2 is Gear C ( $50$ teeth). Gear C meshes directly with Gear D ( $25$ teeth) mounted on Shaft 3. Based on this configuration, what is the rotational speed and direction of Shaft 3?

480

RPM, counter-clockwise

480

RPM, clockwise

30

RPM, counter-clockwise

120

RPM, counter-clockwise

Show answer & explanation

Answer: $480$ RPM, counter-clockwise

Answer

The output shaft rotates at

480

RPM in a counter-clockwise direction.

In a compound gear train, mechanical advantage and speed ratios are multiplied across stages. In the first stage (Gears A to B), a

40

-tooth gear drives a

20

-tooth gear, doubling the speed to

240

RPM and reversing the direction to clockwise. Both gears on Shaft 2 rotate together. In the second stage (Gears C to D), a

50

-tooth gear drives a

25

-tooth gear, doubling the speed again to

480

RPM and reversing the direction back to counter-clockwise.

Step-by-Step Solution

1

Calculate the rotational speed of Shaft 2.

Speed =

120 \times (40 / 20) = 240

RPM.

The speed ratio between meshing gears is inversely proportional to their tooth count. A smaller driven gear rotates faster than the driving gear.

2

Determine the rotational direction of Shaft 2.

Clockwise.

When two external gears mesh, they rotate in opposite directions. Since Shaft 1 is counter-clockwise, Shaft 2 must be clockwise. Because Gears B and C are on the same shaft, Gear C also rotates at

240

RPM clockwise.

3

Calculate the rotational speed of Shaft 3.

Speed =

240 \times (50 / 25) = 480

RPM.

Applying the speed ratio principle again from Gear C (driving) to Gear D (driven).

4

Determine the rotational direction of Shaft 3.

Counter-clockwise.

Gear C (clockwise) meshes with Gear D, forcing Gear D to rotate in the opposite direction.

Key Concept

Compound Gear Trains and Speed Ratios

Question 4Question →

Match each gear system configuration with its resulting mechanical properties.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The simple train multiplies torque by 4 and reverses direction. The idler train quadruples speed and keeps the same direction. The compound train provides a mechanical advantage of 6 and keeps the same direction. The rack and pinion converts rotational motion to linear motion.

Each specific gear arrangement produces distinct mechanical outcomes based on the ratio of teeth between the driving and driven gears, the number of intermediary gears, and the physical shape of the gears involved.

Step-by-Step Solution

1

Determine the mechanical properties of the simple train.

Matches with: Torque is multiplied by 4; rotational direction is reversed.

A 15-tooth gear driving a 60-tooth gear has a ratio of 4:1. The driven gear is 4 times larger, multiplying torque by 4. Two meshing gears turn in opposite directions.

2

Determine the mechanical properties of the idler train.

Matches with: Output speed is 4 times the input speed; rotational direction is unchanged.

The 25-tooth idler gear does not change the ratio. The 60-tooth drive gear directly relates to the 15-tooth driven gear, meaning the output is 1/4 the size and spins 4 times as fast. An odd number of gears (3) preserves the rotational direction.

3

Determine the mechanical properties of the compound train.

Matches with: Overall mechanical advantage is 6; final gear rotates in the same direction as the input gear.

Calculate the ratio of each pair: 40/20 = 2, and 30/10 = 3. Multiply them: 2 * 3 = 6. This is the mechanical advantage. There are two gear meshes, causing the direction to reverse twice, returning to the original input direction.

4

Determine the mechanical properties of the rack and pinion.

Matches with: Rotational motion is converted into linear motion.

A round pinion turning against a straight rack is the standard mechanism for converting rotational motion into linear motion.

Key Concept

Calculating gear ratios and tracking rotational direction across simple, idler, compound, and rack-and-pinion trains.

Question 5Question →

A motorized mixer uses two meshing gears to adjust the mixing speed. The driving gear, which is attached to the motor, has $12$ teeth and spins at $150$ RPM. It meshes directly with a driven gear that has $36$ teeth. What is the rotational speed of the driven gear in RPM?

Show answer & explanation

Answer: 50

Answer

50

The driven gear has three times as many teeth as the driving gear (

36

vs

12

). Because gears have an inverse relationship between size and speed, the larger driven gear will rotate at one-third the speed of the driving gear (

150 \div 3 = 50

RPM).

Step-by-Step Solution

1

State the gear speed formula

T_1 \times S_1 = T_2 \times S_2

To establish the inverse relationship between the number of gear teeth and rotational speed

2

Substitute the given values into the formula

12 \times 150 = 36 \times S_2

To set up the equation with the known tooth counts and driving speed

3

Solve for the unknown driven speed (

S_2

)

S_2 = \frac{1800}{36} = 50

To find the final RPM of the driven gear

Key Concept

The rotational speed of meshing gears is inversely proportional to their number of teeth.

Question 6Question →

A portable hand-cranked emergency generator utilizes a compound gear train to step up the rotational speed of its internal rotor. The hand crank is directly attached to the driving gear (Gear A), which has $60$ teeth. Gear A meshes with Gear B, which has $15$ teeth. Gear B is fixed to the same solid shaft as Gear C, which has $45$ teeth. Finally, Gear C meshes with Gear D, which has $10$ teeth and is attached to the generator's rotor.

If a person turns the hand crank at a steady speed of $40\text{ RPM}$ , what is the resulting speed of the generator's rotor in $\text{RPM}$ ?

Show answer & explanation

Answer: 720

Answer

720

In a compound gear train, the overall mechanical advantage (or speed ratio) is found by evaluating each meshing pair separately. The first pair (A to B) increases the speed by a factor of

4

(since

60/15 = 4

). The input speed is

40\text{ RPM}

, so Gear B spins at

160\text{ RPM}

. Because Gear B and Gear C are fixed to the same shaft, Gear C also spins at

160\text{ RPM}

. The second meshing pair (C to D) increases the speed by a factor of

4.5

(since

45/10 = 4.5

). Multiplying Gear C's speed by this ratio gives

160 \times 4.5 = 720\text{ RPM}

.

Step-by-Step Solution

1

Determine the rotational speed of Gear B.

160\text{ RPM}

Gear A (

60

teeth) drives Gear B (

15

teeth). The speed multiplier is

60 / 15 = 4

. Therefore, Gear B spins at

40 \times 4 = 160\text{ RPM}

.

2

Determine the rotational speed of Gear C.

160\text{ RPM}

Gears mounted on the exact same solid shaft rotate at the same speed, regardless of their size.

3

Determine the rotational speed of Gear D (the rotor).

720\text{ RPM}

Gear C (

45

teeth) drives Gear D (

10

teeth). The speed multiplier is

45 / 10 = 4.5

. Therefore, Gear D spins at

160 \times 4.5 = 720\text{ RPM}

.

Key Concept

Compound Gear Train Speed Ratios

Question 7Question →

Based on fundamental mechanical principles, match each basic gear configuration with its resulting effect on the output gear.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct pairings connect gear size relationships to their speed/torque trade-offs, and gear train arrangements to their rotational direction outcomes.

The correct pairings follow the fundamental laws of gear mechanics: size differences dictate speed and torque tradeoffs (larger driven gears increase torque, smaller driven gears increase speed), while the number of gears determines rotation direction (even numbers reverse direction, odd numbers maintain it).

Step-by-Step Solution

1

Analyze the size relationship between the driving and driven gears in the first two configurations.

A smaller driver yields lower speed but higher torque. A larger driver yields higher speed but lower torque.

Torque and speed have an inverse relationship determined by the gear ratio.

2

Evaluate the effect of meshing identical gears.

Identical gears do not change speed or torque, but they do reverse the direction of rotation.

Adjacent meshing gears must always spin in opposite directions, and a 1:1 size ratio means no mechanical advantage is gained or lost.

3

Determine the impact of an idler gear.

An idler gear ensures the output gear spins in the same direction as the input gear.

The idler acts as a middle step, reversing the opposite rotation back to the original direction.

Key Concept

Basic Gear Relationships and Mechanical Advantage

Estimated Time:1m 0s

Question 8Question →

In a simple mechanical drive system, a small driving gear with 10 teeth meshes directly with a larger driven gear that has 30 teeth. If the driving gear is spinning clockwise at $120\text{ RPM}$ , what is the rotational speed and direction of the driven gear?

40\text{ RPM}

, counterclockwise

360\text{ RPM}

, counterclockwise

40\text{ RPM}

, clockwise

360\text{ RPM}

, clockwise

Show answer & explanation

Answer: $40\text{ RPM}$ , counterclockwise

Answer

The driven gear will rotate at

40\text{ RPM}

in a counterclockwise direction.

The correct answer accurately applies both fundamental rules of simple two-gear trains: speed reduction and direction reversal. Because the driven gear has three times as many teeth (30 vs 10), it turns at one-third the speed (40 RPM). Because it meshes directly with the clockwise-turning driving gear, it must turn counterclockwise.

Step-by-Step Solution

1

Determine the direction of rotation for the driven gear.

Counterclockwise

When two external gears mesh directly, they rotate in opposite directions. Since the driving gear rotates clockwise, the driven gear must rotate counterclockwise.

2

Calculate the speed ratio and the output speed.

40\text{ RPM}

The speed of the driven gear is inversely proportional to its number of teeth. The ratio of driving teeth to driven teeth is 10/30 (or 1/3). Multiplying the input speed (

120\text{ RPM}

) by this ratio gives

120 \times (1/3) = 40\text{ RPM}

.

Key Concept

Two adjacent meshing gears always rotate in opposite directions, and a larger driven gear turns slower than a smaller driving gear in direct proportion to their tooth counts.

Estimated Time:45s

Question 9Question →

A small water pump uses a direct gear drive system. The driving gear, attached to an electric motor, has $20$ teeth and spins at $300\text{ rpm}$ . It meshes directly with a driven gear on the pump shaft that has $60$ teeth. What is the rotational speed of the driven gear in rpm?

Show answer & explanation

Answer: 100

Answer

100 rpm

Because the driven gear has three times as many teeth as the driving gear (

60

compared to

20

), it requires three times the effort to turn. Therefore, it will rotate at exactly one-third the speed of the driving gear. Dividing the driving speed of

300\text{ rpm}

by

3

yields

100\text{ rpm}

.

Step-by-Step Solution

1

Recall the fundamental gear relationship formula.

S_1 \times T_1 = S_2 \times T_2

The product of the speed and number of teeth of the driving gear equals the product of the speed and number of teeth of the driven gear.

2

Substitute the given values into the formula.

300 \times 20 = S_2 \times 60

We are given the driving gear speed (

300\text{ rpm}

) and teeth (

20

), along with the driven gear teeth (

60

).

3

Solve for the driven gear speed (

S_2

).

S_2 = \frac{6000}{60} = 100\text{ rpm}

Isolating

S_2

provides the final rotational speed of the driven gear.

Key Concept

The speed of a driven gear is inversely proportional to its number of teeth compared to the driving gear.

Question 10Question →

A primary driving gear with 20 teeth operates at a speed of $120\text{ rpm}$ . Match each potential driven gear, identified by its tooth count, to the resulting output speed it would produce when directly meshed with this driving gear.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The 10-tooth gear matches to

240\text{ rpm}

, the 20-tooth gear matches to

120\text{ rpm}

, the 40-tooth gear matches to

60\text{ rpm}

, and the 60-tooth gear matches to

40\text{ rpm}

.

The correct matches are derived using the fundamental gear ratio principle: the speed of a driven gear is inversely proportional to its number of teeth compared to the driving gear.

Step-by-Step Solution

1

Calculate the constant proportional value of the driving gear by multiplying its teeth by its speed.

20 \text{ teeth} \times 120\text{ rpm} = 2400

In a meshed gear system, the product of a gear's tooth count and its rotational speed remains constant for all meshing gears (

T_1 \times S_1 = T_2 \times S_2

).

2

Determine the output speed for each driven gear by dividing the constant value by its respective tooth count.

2400 \div 10 = 240

;

2400 \div 20 = 120

;

2400 \div 40 = 60

;

2400 \div 60 = 40

.

This isolates the unknown speed variable (

S_2

) for each specific gear configuration.

Key Concept

Gear Ratios and Speed Inverse Proportionality

Question 11Question →

Review the following gear train configurations. Match each specific gear arrangement to its resulting mechanical outcome or primary functional advantage.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Match the small driving gear to torque multiplication, the large driving gear to speed multiplication, the idler setup to identical direction/speed, and the worm gear to extreme reduction/self-locking.

Each arrangement fundamentally alters mechanical power in a distinct way: small-to-large increases torque, large-to-small increases speed, idlers are strictly for directional matching, and worm gears provide self-locking high-reduction.

Step-by-Step Solution

1

Analyze the 15-tooth driving to 60-tooth driven gear arrangement.

It operates as a step-down gear system with a 1:4 ratio.

A smaller driving gear turning a larger driven gear inherently increases torque at the expense of rotational speed.

2

Analyze the 60-tooth driving to 15-tooth driven gear arrangement.

It operates as a step-up gear system with a 4:1 ratio.

A larger driving gear turning a smaller driven gear increases output rotational speed but reduces the available torque.

3

Analyze the two 30-tooth gears connected by an idler.

The output gear spins at the exact same speed as the input gear, and in the same rotational direction.

The intermediate idler gear reverses the rotational direction twice, ensuring input and output spin identically. The idler's size has no mathematical effect on the overall 1:1 ratio between the identical 30-tooth gears.

4

Analyze the worm and spur gear setup.

It drastically drops speed and cannot be easily back-driven.

A worm drive behaves like a continuous screw; a single full rotation of the worm may only advance the spur gear by one tooth, yielding massive reduction. Additionally, the angle typically prevents the spur gear from turning the worm.

Key Concept

Mechanical Advantage and Function of Gear Trains

Question 12Question →

A motor drives a small pinion gear with 10 teeth, which is meshed directly with a larger bull gear having 40 teeth. Compared to the small driving gear, which of the following correctly describes the output of the large driven gear?

It will rotate slower and produce more torque.

It will rotate faster and produce more torque.

It will rotate faster and produce less torque.

It will rotate slower and produce less torque.

Show answer & explanation

Answer: It will rotate slower and produce more torque.

Answer

The large driven gear will rotate slower and produce more torque compared to the small driving gear.

In a gear train, when a small gear drives a larger gear, the system is stepping down the speed. Because the driven gear has more teeth, it revolves less frequently than the driving gear. However, due to the conservation of energy (ignoring friction), this reduction in speed provides a mechanical advantage, meaning the output torque (turning force) is increased.

Step-by-Step Solution

1

Analyze the size relationship between the driving gear and the driven gear.

The driving gear has 10 teeth, and the driven gear has 40 teeth. The driven gear is larger.

Gear size determines the mechanical advantage and the speed ratio.

2

Determine the effect of size on rotational speed.

Because the driven gear is 4 times larger (40/10 = 4), it will take 4 revolutions of the smaller gear to turn the larger gear once. Therefore, the driven gear rotates slower.

A smaller gear must turn multiple times to advance the many teeth of a larger gear through one full rotation.

3

Determine the effect on torque (turning force).

The decrease in speed is accompanied by a proportional increase in torque. The torque is multiplied by 4.

In simple machines like gear trains, trading distance (or speed) results in a gain in force (or torque), conserving mechanical power.

Key Concept

Mechanical Advantage in Gears

Question 13Question →

Inside a wind-up toy, a main spring rotates a driving gear with 60 teeth at a speed of 10 RPM. This gear directly meshes with a smaller driven gear that powers the toy's legs. If the legs require the driven gear to spin at 40 RPM to function properly, how many teeth must the driven gear have?

Show answer & explanation

Answer: 15

Answer

15 teeth

The correct answer is derived using the principle that the product of the number of teeth and rotational speed must be equal for two meshed gears (

60 \times 10 = 15 \times 40

). This confirms the driven gear must have 15 teeth to rotate at 40 RPM.

Step-by-Step Solution

1

Identify the relationship between gear teeth and rotational speed.

The governing formula is

T_1 \times S_1 = T_2 \times S_2

, where T represents the number of teeth and S represents the speed in RPM.

Gear speed is inversely proportional to the number of teeth.

2

Substitute the given numerical values into the equation.

60 \times 10 = T_2 \times 40

Applying the known driving gear parameters (60 teeth, 10 RPM) and the target speed for the driven gear (40 RPM).

3

Calculate the unknown number of teeth for the driven gear.

600 = T_2 \times 40

, which gives

T_2 = 15

Isolating the variable

T_2

yields the required tooth count for the mechanism to function correctly.

Key Concept

Gear Ratio and Speed Calculations

Question 14Question →

Match each gear arrangement with its resulting mechanical effect on speed, torque, or rotational direction.

Click a left item, then click its matching right item

Show answer & explanation

Answer

A small driver to a large driven gear decreases speed and increases torque. A large driver to a small driven gear increases speed and decreases torque. Two directly meshed gears rotate in opposite directions. An idler gear between two gears allows the input and output to rotate in the same direction.

Each physical gear arrangement corresponds to a single, consistent mechanical law: size differences alter the speed/torque ratio inversely, while the number of meshing points dictates rotational direction.

Step-by-Step Solution

1

Analyze the size relationship for the first two scenarios.

A smaller driver turning a larger gear trades speed for torque (gear reduction). A larger driver turning a smaller gear trades torque for speed (overdrive).

Understanding the fundamental trade-off between speed and torque is required to match size differences with output changes.

2

Analyze the rotational direction for direct mesh versus an idler train.

Direct mesh always reverses direction. Adding a single idler gear reverses it again, making the output match the input direction.

Counting the number of gears in a train determines the final direction of rotation.

Key Concept

Basic Gear Ratios and Rotational Direction

Estimated Time:1m 0s

Question 15Question →

An industrial dough mixer is driven by a three-gear system. The motor is connected to Gear A (the driving gear), which has 15 teeth and rotates counter-clockwise at $300\text{ RPM}$ . Gear A meshes with an intermediate idler Gear B, which has 45 teeth. Gear B then meshes with Gear C (the final driven gear), which has 75 teeth and turns the mixer blade. What is the rotational speed and direction of Gear C?

60\text{ RPM}

, counter-clockwise

60\text{ RPM}

, clockwise

100\text{ RPM}

, counter-clockwise

1500\text{ RPM}

, counter-clockwise

Show answer & explanation

Answer: $60\text{ RPM}$ , counter-clockwise

Answer

The driven gear will rotate at

60\text{ RPM}

in the counter-clockwise direction.

The correct answer accurately determines both speed and direction. In a simple gear train, the idler gear (Gear B) does not change the final speed ratio. The overall ratio is found by comparing the driving gear (15 teeth) to the final driven gear (75 teeth). The ratio is

15/75

, or

1/5

. Therefore, Gear C spins at

1/5

the speed of Gear A (

300 \times 1/5 = 60\text{ RPM}

). For direction, meshing gears alternate: Gear A (counter-clockwise) drives Gear B (clockwise), which in turn drives Gear C (counter-clockwise).

Step-by-Step Solution

1

Determine the effect of the intermediate Gear B.

Gear B acts as an idler gear. It changes the direction of rotation between Gear A and Gear C, but does not affect the overall speed ratio of the system.

In a simple gear train, intermediate gears only bridge the gap and alter direction; the final speed is dictated exclusively by the first and last gears.

2

Calculate the final rotational speed of Gear C.

Speed ratio = (Teeth on Driving Gear) / (Teeth on Driven Gear) =

15 / 75 = 1/5

. The speed of Gear C is

300\text{ RPM} \times (1/5) = 60\text{ RPM}

.

Rotational speed is inversely proportional to the number of gear teeth. A larger driven gear will rotate slower than a smaller driving gear.

3

Determine the final direction of rotation for Gear C.

Gear A rotates counter-clockwise (CCW). Meshing Gear B rotates clockwise (CW). Meshing Gear C rotates counter-clockwise (CCW).

Adjacent meshing gears always rotate in opposite directions.

Key Concept

Idler gears change rotation direction but not the overall speed ratio, and larger driven gears result in a slower rotational speed.

Estimated Time:1m 0s

Question 16Question →

A motorized telescope mount uses a compound gear system to adjust its viewing angle. The driving gear, Gear W, has 24 teeth and rotates counter-clockwise at $400\text{ RPM}$ . Gear W meshes directly with Gear X, which has 96 teeth. Gear X and Gear Y are rigidly mounted on the same intermediate shaft. Gear Y has 30 teeth and meshes with the final output gear, Gear Z, which has 120 teeth. What is the rotational speed and direction of Gear Z?

25\text{ RPM}

, counter-clockwise

25\text{ RPM}

, clockwise

400\text{ RPM}

, counter-clockwise

80\text{ RPM}

, clockwise

Show answer & explanation

Answer: $25\text{ RPM}$ , counter-clockwise

Answer

The final output gear, Gear Z, rotates at

25\text{ RPM}

in the counter-clockwise direction.

In a compound gear system, the overall speed ratio is determined by analyzing each meshing pair. The first pair (W to X) reduces the speed from

400\text{ RPM}

to

100\text{ RPM}

(

400 \times 24/96

) and reverses the direction from counter-clockwise to clockwise. Since Gear Y shares a shaft with Gear X, it also rotates at

100\text{ RPM}

clockwise. The second meshing pair (Y to Z) further reduces the speed from

100\text{ RPM}

to

25\text{ RPM}

(

100 \times 30/120

) and reverses the direction again, making the final output counter-clockwise.

Step-by-Step Solution

1

Calculate the rotational speed and direction of Gear X.

Speed of Gear X is

100\text{ RPM}

, rotating clockwise.

Gear X is driven by Gear W. The speed ratio is

24/96 = 1/4

.

400\text{ RPM} \times (1/4) = 100\text{ RPM}

. Meshing gears rotate in opposite directions, so Gear X rotates clockwise.

2

Determine the speed and direction of Gear Y.

Speed of Gear Y is

100\text{ RPM}

, rotating clockwise.

Gear Y is rigidly mounted on the same shaft as Gear X, meaning they share the exact same rotational speed and direction.

3

Calculate the rotational speed and direction of Gear Z.

Speed of Gear Z is

25\text{ RPM}

, rotating counter-clockwise.

Gear Z is driven by Gear Y. The speed ratio is

30/120 = 1/4

.

100\text{ RPM} \times (1/4) = 25\text{ RPM}

. Meshing gears rotate in opposite directions, so Gear Z rotates counter-clockwise.

Key Concept

Compound Gear Trains and Rotational Direction

Question 17Question →

Match the following types of gear components to their primary mechanical function within a transmission system.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Rack and pinion maps to converting rotational to linear motion. Worm gear maps to providing drastic speed reduction and preventing back-driving. Bevel gear maps to changing the axis of rotation by 90 degrees. Idler gear maps to reversing rotational direction without changing the final output speed ratio.

Each gear type serves a distinct mechanical purpose: rack and pinions handle linear conversion, worm gears manage high reduction and locking, bevel gears handle angular power transmission, and idlers handle direction reversal without ratio changes.

Step-by-Step Solution

1

Identify the unique function of a rack and pinion system.

Matches with converting rotational motion into linear motion.

The circular pinion rolls along the flat rack, pushing it in a straight line, which is unique among these options.

2

Identify the primary characteristic of a worm gear drive.

Matches with providing drastic speed reduction and preventing back-driving.

The screw-like thread of the worm advances the gear by one tooth per revolution, giving high reduction, and friction usually prevents reverse operation.

3

Identify the application of a bevel gear set.

Matches with changing the axis of rotation by 90 degrees between intersecting shafts.

The conical shape of bevel gears allows them to mesh at an angle, most commonly 90 degrees, allowing perpendicular power transmission.

4

Identify the purpose of an idler gear.

Matches with reversing the rotational direction without changing the final output speed ratio.

An intermediate gear only changes the spin direction of the subsequent gear; its tooth count cancels out in the overall ratio calculation.

Key Concept

Functions of specialized gear types in power transmission

Question 18Question →

A conveyor system uses a compound gear train to reduce motor speed. The driving motor turns Gear A (20 teeth) clockwise at $240\text{ rpm}$ . Gear A meshes with Gear B (60 teeth). Gear B shares a solid axle with Gear C (10 teeth), meaning they rotate together. Gear C meshes with Gear D (40 teeth), which drives the conveyor belt. What is the rotational speed and direction of Gear D?

20\text{ rpm}

, clockwise

20\text{ rpm}

, counter-clockwise

120\text{ rpm}

, counter-clockwise

2880\text{ rpm}

, clockwise

Show answer & explanation

Answer: $20\text{ rpm}$ , clockwise

Answer

Gear D rotates at

20\text{ rpm}

, clockwise.

In a compound gear system, the total speed reduction is the product of the individual gear pair ratios. The first pair reduces the speed from

240\text{ rpm}

to

80\text{ rpm}

and reverses direction to counter-clockwise. The second pair reduces the

80\text{ rpm}

speed to

20\text{ rpm}

and reverses direction back to clockwise.

Step-by-Step Solution

1

Calculate the speed and direction of Gear B.

Gear B rotates at

80\text{ rpm}

counter-clockwise.

Gear B has three times as many teeth as Gear A (60 vs 20), so it spins at one-third the speed (

240 / 3 = 80

). Meshing gears turn in opposite directions.

2

Determine the speed and direction of Gear C.

Gear C rotates at

80\text{ rpm}

counter-clockwise.

Gears mounted on the same solid axle rotate at the exact same speed and in the same direction.

3

Calculate the speed and direction of Gear D.

Gear D rotates at

20\text{ rpm}

clockwise.

Gear D has four times as many teeth as Gear C (40 vs 10), so it spins at one-quarter the speed of Gear C (

80 / 4 = 20

). Meshing gears turn in opposite directions.

Key Concept

Compound Gear Trains and Speed Reduction

Question 19Question →

A hand-cranked emergency power generator uses a two-stage compound gear train to increase the rotational speed of its rotor. The hand crank is connected directly to the driving gear, Gear A, which has $60$ teeth. Gear A meshes with Gear B, which has $15$ teeth. Gear B shares a solid intermediate shaft with Gear C, which has $40$ teeth. Finally, Gear C meshes with Gear D on the generator's rotor shaft, which has $10$ teeth.

If a user turns the hand crank at a steady rate of $30\text{ rpm}$ , what is the resulting rotational speed of the generator rotor in $\text{rpm}$ ?

Show answer & explanation

Answer: 480

Answer

480

The correct answer is 480 because the total speed multiplication of a compound gear train is the product of the individual gear ratios of each stage. Stage 1 has a ratio of 60:15 (a 4:1 multiplier). Stage 2 has a ratio of 40:10 (a 4:1 multiplier). The total multiplier is 4 * 4 = 16. The input speed of 30 rpm multiplied by 16 gives a final output speed of 480 rpm.

Step-by-Step Solution

1

Calculate the speed multiplication factor of the first gear pair.

Factor of 4

Gear A (60 teeth) drives Gear B (15 teeth). The ratio of teeth is 60/15 = 4. Because a larger gear is driving a smaller gear, the rotational speed increases by this factor.

2

Calculate the rotational speed of the intermediate shaft.

120 rpm

Multiply the input speed (30 rpm) by the first stage factor (4). 30 * 4 = 120 rpm. Both Gear B and Gear C spin at this exact rate since they are mounted on the same solid shaft.

3

Calculate the speed multiplication factor of the second gear pair.

Factor of 4

Gear C (40 teeth) drives Gear D (10 teeth). The ratio is 40/10 = 4. Again, a larger gear is driving a smaller one, increasing the speed.

4

Calculate the final rotational speed of the rotor.

480 rpm

Multiply the intermediate shaft speed (120 rpm) by the second stage factor (4). 120 * 4 = 480 rpm.

Key Concept

Calculating output speed in a compound gear train

Question 20Question →

A commercial dough mixer utilizes a three-gear sequence to rotate its mixing hook. The main motor turns the first gear (24 teeth) clockwise at $240\text{ rpm}$ . This gear meshes directly with a smaller intermediate gear (12 teeth), which subsequently drives the final hook gear (72 teeth). What is the resulting rotational speed and direction of the final hook gear?

720\text{ rpm}

, clockwise

80\text{ rpm}

, counter-clockwise

80\text{ rpm}

, clockwise

720\text{ rpm}

, counter-clockwise

Show answer & explanation

Answer: $80\text{ rpm}$ , clockwise

Answer

The final hook gear rotates at

80\text{ rpm}

in a clockwise direction.

The intermediate gear acts as an idler. Therefore, the overall speed ratio depends only on the first (24 teeth) and final (72 teeth) gears. The driven gear is three times larger than the driving gear, so it will rotate at one-third the speed:

240 / 3 = 80\text{ rpm}

. Regarding direction, meshing gears rotate in opposite directions. The first gear is clockwise, the second is counter-clockwise, and the third is clockwise.

Step-by-Step Solution

1

Determine the effect of the intermediate gear on the final speed.

The intermediate gear acts as an idler gear.

An idler gear placed between a driving and driven gear changes the direction of rotation but does not affect the final speed ratio.

2

Calculate the final rotational speed.

Final speed is

80\text{ rpm}

.

The speed is calculated using the ratio of the first and last gears:

\text{Speed} = 240 \times \frac{24}{72} = 240 \times \frac{1}{3} = 80\text{ rpm}

.

3

Determine the final direction of rotation.

The final gear rotates clockwise.

Gear 1 is clockwise, so Gear 2 is counter-clockwise, meaning Gear 3 is clockwise.

Key Concept

Idler Gears and Gear Ratios

Gears and Gear Ratios

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