Gear Ratio RPM Calculator

Gear Ratio: Output Speed (rpm): Output Speed (rad/s): Output Speed (Hz):

1. Gear Ratio

The gear ratio is the ratio of the number of teeth or rotational speeds between two meshing gears. It describes the relationship between the input gear (driving gear) and the output gear (driven gear).

$$ \text{Gear Ratio} = \frac{\text{Output Gear Teeth}}{\text{Input Gear Teeth}} = \frac{\text{Input Speed}}{\text{Output Speed}} $$

- Output Gear Teeth: Number of teeth on the output gear.
- Input Gear Teeth: Number of teeth on the input gear.
- Input Speed: Rotational speed of the input gear.
- Output Speed: Rotational speed of the output gear.

Functions:
- Speed Reduction or Increase: A gear ratio greater than 1 reduces output speed and increases torque, while a gear ratio less than 1 increases output speed and reduces torque.
- Change in Rotation Direction: The direction of rotation can be changed based on the gear configuration.
- Power Transmission: Gear systems are used to transfer power from the input shaft to the output shaft.

2. RPM (Revolutions Per Minute)

RPM is a unit to measure the speed of rotation, indicating the number of complete revolutions an object makes in one minute.

$$ 1\ \text{RPM} = \frac{1}{60}\ \text{Hz} \quad \text{or} \quad 1\ \text{RPM} = 0.104719755\ \text{rad/s} $$

Functions:
- Describes the speed of rotating machinery such as motors, engines, and fans.
- Used to calculate the output speed in gear systems.

3. Relationship Between Gear Ratio and RPM

The gear ratio directly affects the rotational speed (RPM) of the input and output gears. The output RPM can be calculated using the gear ratio.

$$ \text{Output RPM} = \text{Input RPM} \times \text{Gear Ratio} $$

Example:
- Input gear teeth: 20, Output gear teeth: 40, Gear Ratio = $$ \frac{40}{20} = 2 $$.
- Input speed: 100 RPM, Output speed = $$ 100 \times 2 = 200 $$ RPM.

4. Applications

Automobile Transmissions: Different gear ratios are used for acceleration, deceleration, and reversing.
Industrial Machinery: Adjusts speed and torque between motors and loads.
Bicycle Gear Systems: Changes gear ratios to adapt to different riding conditions.

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