Centrifuge
Study centripetal acceleration and g-force in circular motion by varying the rotation speed and radius with the FizziQ Web Centrifuge simulation.
Learning objectives:
The student uses the FizziQ Web Centrifuge simulation to measure centripetal acceleration by varying the rotation speed (at fixed radius) then the radius (at fixed speed). They verify the relationship a = ω²r and connect the results to g-force thresholds.
Level:
Author:
High school
FizziQ Web
Duration (minutes) :
30
What students will do :
- Measure centripetal acceleration for different rotation speeds and radii
- Verify the relationship a = ω²r experimentally
- Understand g-force as the ratio of acceleration to gravitational acceleration
- Plot a versus ω² and a versus r to confirm proportionality
- Calculate the rotation speed needed to simulate different gravity levels
Scientific concepts:
- Centripetal acceleration
- Angular velocity (ω in rad/s)
- Relationship a = ω²r
- G-force
- Uniform circular motion
- Centripetal force
Sensors:
- FizziQ Web Centrifuge simulation
What is required:
- Computer, tablet, or smartphone with FizziQ Web
Experimental procedure:
Open the Centrifuge simulation in FizziQ Web (Experiment → Simulations → Centrifuge).
Part 1 — Effect of speed: set the radius to 5 m. Set the rotation speed to 10 rpm and start the simulation.
Note the centripetal acceleration and g-factor displayed. Stop the recording.
Repeat for speeds 20, 30, 40, 50, and 60 rpm. Create a table: Speed (rpm), ω (rad/s), ω² (rad²/s²), Acceleration (m/s²), g-factor.
To convert: ω (rad/s) = speed (rpm) × 2π / 60. Calculate ω and ω² for each speed.
Plot the graph of acceleration versus ω². Is it a straight line? The slope should equal r = 5 m.
Part 2 — Effect of radius: set the speed to 30 rpm. Vary the radius: 2, 4, 6, 8, 10 m.
Note the centripetal acceleration for each radius. Plot a versus r. The straight line confirms that a is proportional to r.
From your data, determine which speed-radius combination gives a g-factor of 3 (the threshold where untrained people may lose consciousness).
Conclusion: the relationship a = ω²r shows that acceleration depends on the square of speed but only linearly on radius. Doubling the speed quadruples the acceleration.
Expected results:
For r = 5 m: at 10 rpm, ω = 1.05 rad/s, a = 5.5 m/s² (0.56 g). At 30 rpm, ω = 3.14 rad/s, a = 49.3 m/s² (5.0 g). At 60 rpm, ω = 6.28 rad/s, a = 197 m/s² (20.1 g). The graph a(ω²) is a straight line with slope 5 m (equal to the radius). The graph a(r) at 30 rpm is a straight line with slope ω² ≈ 9.87 rad²/s². All results confirm a = ω²r.
Scientific questions:
- Why does the acceleration depend on the square of angular velocity rather than simply on velocity?
- If you double the radius at constant angular velocity, the acceleration doubles. But if you double the tangential speed at constant radius, what happens?
- Why do car passengers feel pushed outward in a turn even though the acceleration is directed inward?
- What radius and rotation speed would be needed to simulate Earth's gravity in a 100 m diameter space station?
- Why are professional centrifuges built with long arms rather than short arms spinning very fast?
- What is the difference between centripetal acceleration and centrifugal force?
Scientific explanations:
In circular motion, an object constantly changes direction even if its speed is constant. This change of direction implies an acceleration directed toward the center of the circle: the centripetal acceleration a = ω²r = v²/r.
The angular velocity ω is expressed in rad/s. To convert from revolutions per minute: ω = N × 2π / 60, where N is the number of rpm.
The g-factor is the ratio of the acceleration experienced to Earth's gravitational acceleration: g-factor = a / 9.81. A g-factor of 1 means the person feels their normal weight. At 3g, they feel three times heavier.
The dependence on ω² has an important consequence: doubling the rotation speed quadruples the acceleration. This is why centrifuges are potentially dangerous: a small speed increase produces a large acceleration increase.
Physiological effects vary with intensity: at 2-3 g, blood pools in the legs. At 4-6 g, an untrained person may lose consciousness. At 9 g, even trained pilots with g-suits are at their limit.
Extension activities:
- Why does the acceleration depend on the square of angular velocity rather than simply on velocity?
- If you double the radius at constant angular velocity, the acceleration doubles. But if you double the tangential speed at constant radius, what happens?
- Why do car passengers feel pushed outward in a turn even though the acceleration is directed inward?
- What radius and rotation speed would be needed to simulate Earth's gravity in a 100 m diameter space station?
- Why are professional centrifuges built with long arms rather than short arms spinning very fast?
- What is the difference between centripetal acceleration and centrifugal force?
Frequently asked questions:
Q: The rotation speed is in rpm but the formulas use ω in rad/s. How do I convert?
R: Multiply the number of revolutions per minute by 2π/60. For example: 30 rpm × 2π/60 = 3.14 rad/s.
Q: Why does the acceleration not depend on the mass of the object?
R: The formula a = ω²r gives the acceleration, which is a kinematic quantity independent of mass. The force needed to maintain circular motion does depend on mass (F = ma), but the acceleration does not.
Q: What is the difference between centripetal and centrifugal force?
R: Centripetal force is the real force directed inward that keeps the object on a circular path. Centrifugal force is an apparent force felt in the rotating reference frame, directed outward. Only centripetal force exists in an inertial frame.
Q: Can the simulation model gravitational effects like blood pooling?
R: No, the simulation only computes the acceleration value. The physiological effects are inferred from the g-factor and known human tolerance thresholds.