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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. It is always directed toward the center of the circle and is responsible for changing the direction of the object's velocity vector while keeping it in circular motion.
The calculator uses the centripetal acceleration formula:
Where:
Explanation: The formula shows that centripetal acceleration increases with the square of angular velocity and directly with the radius of the circular path.
Details: Understanding centripetal acceleration is crucial in various fields including physics, engineering, and astronomy. It's essential for designing safe roads, roller coasters, and understanding planetary motion.
Tips: Enter angular velocity in radians per second and radius in meters. Both values must be positive numbers greater than zero.
Q1: What's the difference between angular velocity and linear velocity?
A: Angular velocity (ω) measures how fast an object rotates (rad/s), while linear velocity (v) measures how fast it moves along the circular path (m/s). They're related by v = ω × r.
Q2: Can centripetal acceleration be negative?
A: No, centripetal acceleration is always positive as it represents magnitude. The direction is always toward the center of the circular path.
Q3: How is centripetal acceleration related to centripetal force?
A: Centripetal force (F_c) is the net force causing centripetal acceleration, related by Newton's second law: F_c = m × a_c, where m is mass.
Q4: What are typical values for centripetal acceleration?
A: Values vary widely - from about 0.03 m/s² for Earth's rotation to over 100 m/s² for high-performance centrifuges.
Q5: Does centripetal acceleration do work on an object?
A: No, centripetal acceleration doesn't do work because it's always perpendicular to the direction of motion, so no energy is transferred.