1. What is Centripetal Acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path, always directed toward the center of rotation. It's a fundamental concept in circular motion physics.

2. How Does the Calculator Work?

The calculator uses the centripetal acceleration formula:

Where:

• \( a_c \) — Centripetal acceleration (m/s²)
• \( \omega \) — Angular velocity (rad/s)
• \( r \) — Radius of circular path (m)

Explanation: The formula shows that centripetal acceleration increases with the square of angular velocity and directly with radius.

3. Importance of Centripetal Acceleration

Details: Understanding centripetal acceleration is crucial for analyzing circular motion in physics, engineering applications, vehicle dynamics, amusement park rides, and planetary motion calculations.

4. Using the Calculator

Tips: Enter angular velocity in radians per second and radius in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

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

Q2: How is angular velocity related to linear velocity?
A: Linear velocity (v) = ω × r, so centripetal acceleration can also be expressed as a_c = v²/r.

Q3: What are typical values for centripetal acceleration?
A: Values vary widely - from very small (planetary motion) to very large (particle accelerators). Earth's centripetal acceleration at equator is about 0.034 m/s².

Q4: Does centripetal acceleration do work on an object?
A: No, because the force is always perpendicular to the direction of motion, so no work is done in uniform circular motion.

Q5: How is this formula used in real-world applications?
A: It's used in designing roads with proper banking angles, calculating forces in rotating machinery, and analyzing satellite orbits.