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Radial Acceleration Formula:
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Radial acceleration (also known as centripetal acceleration) is the acceleration experienced by an object moving in a circular path. It always points toward the center of the circle and is responsible for changing the direction of the object's velocity vector.
The calculator uses the radial acceleration formula:
Where:
Explanation: The formula shows that radial acceleration increases with the square of velocity and decreases with increasing radius of the circular path.
Details: Calculating radial acceleration is essential in various fields including physics, engineering, and transportation. It helps in designing safe curves for roads and railways, analyzing circular motion in mechanical systems, and understanding planetary orbits in astronomy.
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 radial and tangential acceleration?
A: Radial acceleration changes the direction of velocity (toward center), while tangential acceleration changes the magnitude of velocity (along the tangent).
Q2: How does radial acceleration relate to centripetal force?
A: Centripetal force is the net force causing radial acceleration: \( F_c = m \times a_r = \frac{mv^2}{r} \), where m is mass.
Q3: What happens to radial acceleration if velocity doubles?
A: Radial acceleration quadruples since it's proportional to the square of velocity (\( a_r \propto v^2 \)).
Q4: Can radial acceleration be zero?
A: Yes, when either velocity is zero (object at rest) or radius is infinite (straight line motion).
Q5: What are real-world applications of this calculation?
A: Designing roller coasters, calculating banking angles for roads, analyzing satellite orbits, and designing centrifuges.