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Centripetal Acceleration Formula:
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Centripetal acceleration is the acceleration experienced by an object moving in a circular path, directed toward the center of the circle. It is derived from Newton's second law and the force balance in circular motion: \( F = \frac{m v^2}{r} \) and \( a = \frac{F}{m} \).
The calculator uses the centripetal acceleration formula:
Where:
Explanation: The formula shows that centripetal acceleration increases with the square of velocity and decreases with increasing radius of the circular path.
Details: Understanding centripetal acceleration is crucial for analyzing circular motion in physics, engineering applications like vehicle design on curved roads, amusement park rides, and planetary motion calculations.
Tips: Enter velocity in meters per second (m/s) and radius in meters (m). All values must be positive numbers greater than zero.
Q1: What is the difference between centripetal and centrifugal acceleration?
A: Centripetal acceleration is the real acceleration directed toward the center, while centrifugal acceleration is a fictitious force that appears to push objects outward in a rotating reference frame.
Q2: How does mass affect centripetal acceleration?
A: Mass does not appear in the centripetal acceleration formula. While centripetal force depends on mass (\( F = m a_c \)), the acceleration itself is independent of mass.
Q3: What are practical applications of this formula?
A: Used in designing banked curves for roads and railways, calculating satellite orbits, analyzing particle accelerators, and designing centrifuges.
Q4: What happens when velocity doubles?
A: When velocity doubles, centripetal acceleration increases by a factor of four (since acceleration is proportional to velocity squared).
Q5: Can this formula be used for non-uniform circular motion?
A: This formula applies specifically to uniform circular motion. For non-uniform circular motion, tangential acceleration must also be considered.