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 vector changes direction while maintaining constant speed.

2. How Does the Calculator Work?

The calculator uses the centripetal acceleration formula:

Where:

• \( a \) — Centripetal acceleration (m/s²)
• \( v \) — Tangential velocity (m/s)
• \( r \) — Radius of the circular path (m)

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

3. Importance of Centripetal Acceleration

Details: Centripetal acceleration is crucial in understanding circular motion, designing curved roads, analyzing planetary orbits, and engineering rotating machinery. It explains why objects moving in circles experience inward force.

4. Using the Calculator

Tips: Enter velocity in meters per second (m/s) and radius in meters (m). Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

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

Q2: Does centripetal acceleration change the speed of an object?
A: No, centripetal acceleration only changes the direction of velocity, not its magnitude. The speed remains constant in uniform circular motion.

Q3: What provides the centripetal force in different scenarios?
A: Tension in a string for a swinging object, friction for a car turning on a road, gravity for planets orbiting stars, and normal force for objects on rotating platforms.

Q4: Can centripetal acceleration be negative?
A: No, since both velocity squared and radius are positive values, centripetal acceleration is always positive, indicating direction toward the center.

Q5: How does radius affect centripetal acceleration?
A: For the same velocity, smaller radius results in larger centripetal acceleration, meaning tighter turns require greater inward force.