gear A rotates clockwise at 700 rpm, in what direction and at what speed does gear D rotate?
Compound gear train with: 12-tooth Gear A meshed with 60-tooth Gear B, which is coaxial with 12-tooth Gear C, meshed with 84-tooth Gear D.

We are given a compound gear train consisting of four gears: A, B, C, and D. Here's how to solve the problem step by step:

### Step 1: Understanding the gear relationships
- **Gear A** is meshed with **Gear B**.
- **Gear B** is coaxial with **Gear C** (meaning they rotate together, so they share the same rotational speed).
- **Gear C** is meshed with **Gear D**.

This means the power is transmitted from **Gear A** to **Gear D** through two pairs of meshed gears: 
1. Gear A and Gear B
2. Gear C and Gear D.

### Step 2: Direction of rotation
- When two gears are meshed, they rotate in opposite directions.
- Since Gear A rotates **clockwise**, Gear B will rotate **counterclockwise** (opposite direction).
- Since Gear B is coaxial with Gear C, Gear C will also rotate **counterclockwise**.
- Gear C is meshed with Gear D, so Gear D will rotate **clockwise**.

Thus, **Gear D rotates clockwise**.

### Step 3: Speed of rotation
The speed of rotation between two meshed gears is inversely proportional to the number of teeth, following the formula:

\[
\text{Speed ratio between two gears} = \frac{\text{Teeth on driven gear}}{\text{Teeth on driving gear}}
\]

#### Step 3a: Speed of Gear B (and C)
Gear A drives Gear B:
\[
\frac{\text{Speed of B}}{\text{Speed of A}} = \frac{\text{Teeth on A}}{\text{Teeth on B}} = \frac{12}{60} = \frac{1}{5}
\]
Thus, the speed of Gear B is:
\[
\text{Speed of B} = 700 \, \text{rpm} \times \frac{1}{5} = 140 \, \text{rpm}
\]
Since Gear B and Gear C are coaxial, the speed of Gear C is also **140 rpm**.

#### Step 3b: Speed of Gear D
Gear C drives Gear D:
\[
\frac{\text{Speed of D}}{\text{Speed of C}} = \frac{\text{Teeth on C}}{\text{Teeth on D}} = \frac{12}{84} = \frac{1}{7}
\]
Thus, the speed of Gear D is:
\[
\text{Speed of D} = 140 \, \text{rpm} \times \frac{1}{7} = 20 \, \text{rpm}
\]

### Final Answer:
- **Gear D rotates clockwise** at **20 rpm**.

Would you like a detailed breakdown of any part of this solution?

Here are some related questions you might find useful:
1. How do different gear arrangements (e.g., planetary gears) affect rotation speed?
2. What are the applications of compound gear trains in mechanical systems?
3. How do gear ratios influence torque in gear systems?
4. Can you explain how to calculate the mechanical advantage in gear systems?
5. What is the significance of backlash in gear trains?

**Tip**: When calculating gear ratios, remember that speed is inversely proportional to the number of teeth—more teeth mean slower speed but more torque!

Gear A rotates clockwise at 700 rpm, in what direction and at what speed does gear D rotate? Compound gear train with: 12-tooth Gear A meshed with 60-tooth Gear B, which is coaxial with 12-tooth Gear C, meshed with 84-tooth Gear D.

Learn how to calculate the speed and direction of Gear D in a compound gear train involving Gear A rotating at 700 rpm. This problem involves calculating gear ratios, understanding inversely proportional relationships, and applying formulas to solve for speed and rotation. Suitable for Grades 9-12.

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