Centripetal acceleration is the acceleration that keeps an object moving in a circular path. It always points toward the center of the circle.
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How to measure it in class
Steps:
- Attach the smartphone to a string and swing it in a circle
- Record the acceleration
- Observe how acceleration increases with rotation speed
- Verify the relationship with radius and velocity
Formula
ac = v²/r = ω²r
Where:
- ac: centripetal acceleration (m/s²)
- v: tangential velocity (m/s)
- r: radius (m)
- ω: angular velocity (rad/s)
Scientific activities on this topic
Several experiments easily performed with a smartphone or tablet allow you to measure the centripetal acceleration exerted on an object following a uniform circular trajectory:
- Could an astronaut survive if placed in a salad spinner? https://www.fizziq.org/en/activities/astronaut-and-salad-spinner/
- Measuring centripetal acceleration for a pendulum: https://www.fizziq.org/en/activities/leibnitz/
- Demonstrating the relationship between velocity and centripetal acceleration: https://www.fizziq.org/en/activities/in-orbit/
Examples
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The force felt by passengers on a carousel spinning at high speed
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The lean of a cyclist in a turn to compensate for centripetal acceleration
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Laundry pressed against the drum of a washing machine during the spin cycle
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The curved trajectory of a satellite around Earth, maintained by gravity
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A car skidding in a turn taken too fast, when friction is insufficient
FAQ
Q: Does centrifugal force really exist? A: Centrifugal force is not a real force in Newton’s sense. It is a fictitious force that appears in the rotating reference frame. In the ground reference frame, only the centripetal force (directed toward the center) actually exists.
Q: Why is centripetal acceleration directed toward the center? A: Because it must change the direction of velocity without modifying its magnitude. The only direction that changes orientation without modifying the value of velocity is the direction perpendicular to the trajectory, toward the center.
Q: Does centripetal acceleration change the object’s velocity? A: It does not change the value (magnitude) of velocity, but it constantly changes its direction. That is why we speak of uniform circular motion: velocity is constant in magnitude but not in direction.
Q: Can you feel centripetal acceleration? A: Yes. In a car turn or on a carousel, you feel a force pushing outward. What you feel is actually the reaction to the centripetal force exerted by the seat or structure.
Q: How does gravity play the role of centripetal force for the Moon? A: The gravitational force exerted by Earth on the Moon is directed toward Earth’s center. This force provides exactly the centripetal acceleration needed to keep the Moon on its nearly circular orbit.
Related concepts
Centripetal force - Uniform circular motion - Angular velocity - Acceleration - Inertia - Gravitation - Accelerometer