1. What is Centripetal Acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path, directed toward the center of the circle. It describes how quickly the velocity direction changes during circular motion.

2. How Does the Calculator Work?

The calculator uses the centripetal acceleration formula:

Where:

• \( a_c \) — Centripetal acceleration (m/s²)
• \( r \) — Radius of circular path (m)
• \( T \) — Period of revolution (s)
• \( \pi \) — Mathematical constant (3.1416)

Explanation: This formula calculates the acceleration required to keep an object moving in a circular path of radius r with period T.

3. Importance of Centripetal Acceleration

Details: Centripetal acceleration is fundamental in understanding circular motion, planetary orbits, vehicle dynamics on curved paths, and various engineering applications involving rotational systems.

4. Using the Calculator

Tips: Enter the radius in meters and period in seconds. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between centripetal and centrifugal acceleration?
A: Centripetal acceleration is the actual inward acceleration toward the center, while centrifugal is the apparent outward force felt in a rotating reference frame.

Q2: How does radius affect centripetal acceleration?
A: For constant period, centripetal acceleration increases linearly with radius. For constant speed, it decreases with increasing radius.

Q3: What are typical values of centripetal acceleration?
A: Values range from very small (planetary orbits) to very large (centrifuges). Earth's centripetal acceleration at equator is about 0.034 m/s².

Q4: Can this formula be used for any circular motion?
A: Yes, this formula applies to any uniform circular motion where the period is known.

Q5: What if I know speed instead of period?
A: Use the alternative formula: \( a_c = \frac{v^2}{r} \), where v is the tangential speed.