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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 rotation. It's essential for maintaining circular motion and is perpendicular to the object's velocity vector.
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: Calculating centripetal acceleration is crucial in various fields including physics, engineering, astronomy, and vehicle dynamics. It helps in designing safe curves for roads and railways, analyzing planetary motion, and understanding circular motion in mechanical systems.
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.
Q1: What's the difference between centripetal and centrifugal acceleration?
A: Centripetal acceleration is the actual acceleration toward the center that keeps an object in circular motion, while centrifugal acceleration is the apparent outward force experienced in a rotating reference frame.
Q2: How does centripetal acceleration relate to centripetal force?
A: Centripetal force is the net force causing centripetal acceleration, related by Newton's second law: F = m × a_c, where m is mass.
Q3: What are typical values of centripetal acceleration?
A: Values vary widely - from about 0.03 m/s² for Earth's rotation to over 50 m/s² for Formula 1 cars taking sharp turns.
Q4: Can centripetal acceleration be negative?
A: No, since both velocity squared and radius are always positive, centripetal acceleration is always positive, indicating direction toward the center.
Q5: How is this formula derived?
A: The formula is derived from the geometry of circular motion and the relationship between angular velocity (ω) and tangential velocity (v = ωr).