Speed Of Bigger Pulley Given Speed Of Smaller Pulley Calculator

Formula Used:

\[ n_2 = d \times \left( \frac{n_1}{D} \right) \]

Diameter of Small Pulley (d):

Speed of Smaller Pulley (n₁):

rad/s

Diameter of Big Pulley (D):

Speed of Larger Pulley (n₂):

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1. What is the Speed of Larger Pulley Formula?

The formula calculates the speed of a larger pulley in a belt drive system based on the diameters of both pulleys and the speed of the smaller pulley. It demonstrates the inverse relationship between pulley diameter and rotational speed in a belt drive system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ n_2 = d \times \left( \frac{n_1}{D} \right) \]

Where:

\( n_2 \) — Speed of Larger Pulley (rad/s)
\( d \) — Diameter of Small Pulley (m)
\( n_1 \) — Speed of Smaller Pulley (rad/s)
\( D \) — Diameter of Big Pulley (m)

Explanation: The formula shows that the speed of the larger pulley is directly proportional to the diameter of the smaller pulley and the speed of the smaller pulley, and inversely proportional to the diameter of the larger pulley.

3. Importance of Pulley Speed Calculation

Details: Accurate pulley speed calculation is crucial for designing mechanical systems, ensuring proper power transmission, maintaining optimal machine performance, and preventing equipment damage due to incorrect speed ratios.

4. Using the Calculator

Tips: Enter the diameter of the small pulley in meters, speed of the smaller pulley in rad/s, and diameter of the big pulley in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Why does pulley diameter affect speed?
A: In belt drive systems, the linear speed of the belt remains constant. Therefore, larger pulleys rotate slower and smaller pulleys rotate faster to maintain the same linear belt speed.

Q2: What is the speed ratio in pulley systems?
A: The speed ratio is the ratio of driver pulley speed to driven pulley speed, which equals the ratio of driven pulley diameter to driver pulley diameter.

Q3: Can this formula be used for different units?
A: Yes, but all measurements must use consistent units. The calculator currently uses meters for diameters and rad/s for speeds.

Q4: What are typical applications of this calculation?
A: This calculation is used in conveyor systems, automotive engines, industrial machinery, and any mechanical system using belt drives for power transmission.

Q5: How does belt tension affect the calculation?
A: The formula assumes ideal conditions with no belt slip. In real applications, belt tension and potential slip should be considered for more accurate results.